THE  MAJOR  TACTICS  OF  CHESS 


THE      ::;v-;;: :-    :/. 

MAJOR  TACTICS  OF  CHESS 

A  TREATISE   ON  EVOLUTIONS 

THE    PROPER    EMPLOYMENT    OF    THE    FORCES 

IN  STRATEGIC,  TACTICAL,  AND 

LOGISTIC   PLANES 


BY 

FRANKLIN  K.  YOUNG 

»* 

AUTHOR  OF  "THE  MINOR  TACTICS  OF  CHESS"  AND 
"THE  GRAND  TACTICS  OF  CHESS" 


BOSTON 

LITTLE,   BROWN,   AND    COMPANY 
1919 


Copyright,  1898, 
BY  FRANKLIN  K.  YOUNG. 

All  rights  reserved. 


Printed  by 
Louis  E.  CROSSCUP,  BOSTON,  U.S.A. 


PREFACE. 


,  the  second  volume  of  the  Chess  Strategetics 
series,  may  not  improperly  be  termed  a  book  of 
chess  tricks. 

Its  purpose  is  to  elucidate  those  processes  upon  which 
every  ruse,  trick,  artifice,  and  stratagem  known  in  chess- 
play,  is  founded ;  consequently,  this  treatise  is  devoted 
to  teaching  the  student  how  to  win  hostile  pieces,  to 
queen  his  pawns,  and  to  checkmate  the  adverse  king. 

All  the  processes  herein  laid  down  are  determinate, 
and  if  the  opponent  becomes  involved  in  any  one  of  them, 
he  should  lose  the  game. 

Each  stratagem  is  illustrative  of  a  principle  of  Tac- 
tics ;  it  takes  the  form  of  a  geometric  proposition,  and  in 
statement,  setting  and  demonstration,  is  mathematically 
exact. 

The  student,  having  once  committed  these  plots  and 
counter-plots  to  memory,  becomes  equipped  with  a  tech- 
nique whereby  he  is  competent  to  project  and  to  execute 
any  design  and  to  detect  and  foil  every  machination  of 
his  antagonist. 

BOSTON,  1898. 


CONTENTS. 


PAGE 

INTRODUCTORY xv 

MAJOR  TACTICS 3 

Definition  of ...•.  3 

Grand  Law  of 3 

Evolutions  of 3 

GEOMETRIC  SYMBOLS 4 

Of  the  Pawn 5 

"      Knight 6 

"      Bishop 7 

"      Rook 8 

"      Queen 9 

"      King 10 

SUB-GEOMETRIC  SYMBOLS       11 

Of  the  Pawn 12 

"      Knight 13 

«      Bishop 14 

«      Rook 15 

"      Queen       16 

"      King 17 

LOGISTIC  SYMBOLS 18 

Of  the  Pawn 18 

"      Knight       19 

«      Bishop 20 

«      Rook 21 

«      Queen       22 

«      King 23 

GEOMETRIC  PLANES       24 

Tactical 25 

Logistic 26 

Strategic 27 


x  CONTENTS. 

PAG* 

PLANE  TOPOGRAPHY  (a) 28 

Zone  of  Evolution 31 

Kindred  Integers 32 

Hostile  Integers 33 

Prime  Tactical  Factor 34 

Supporting  Factor 35 

Auxiliary  Factor 36 

Piece  Exposed 37 

Disturbing  Factor 38 

Primary  Origin 39 

Supporting  Origin 40 

Auxiliary  Origin 41 

Point  Material 42 

Point  of  Interference 43 

Tactical  Front 44 

Front  Offensive 45 

Front  Defensive 46 

Supporting  Front 47 

Front  Auxiliary 48 

Front  of  Interference 48 

Point  of  Co-operation 49 

Point  of  Command 50 

Point  Commanded 51,  52 

Prime  Radius  of  Offence 53 

Tactical  Objective 54 

Tactical  Sequence 54 

TACTICAL  PLANES 55 

Simple 56 

Compound 57 

Complex 58,  59 

LOGISTIC  PLANES 60 

Simple 61 

Compound 62 

Complex 63 

PLANE  TOPOGRAPHY  (5) 64 

The  Logistic  Horizon 64-66 

Pawn  Altitude 67 

Point  of  Junction 68 


CONTENTS.  xi 

PLANE  TOPOGRAPHY  (continued'). 

Square  of  Progression 69 

Corresponding  Knight's  Octagon 70 

Point  of  Resistance 71 

STRATEGIC  PLANES 72 

Simple 73 

Compound 74,  75 

Complex 76 

PLANE  TOPOGRAPHY  (c) 77 

The  Objective  Plane 78 

Objective  Plane  Commanded 79 

Point  of  Lodgment 80 

Point  of  Impenetrability 81 

Like  Points 82 

Unlike  Points 83 

BASIC  PROPOSITIONS  OF  MAJOR  TACTICS 84 

Proposition  I 85 

•«  II 91 

III 97 

"  IV 103 

«  V 110 

VI Ill 

VII 112 

«  VIII 113 

"  IX 118 

«  X 119 

XI 121 

«  XII 123 

SIMPLE  TACTICAL  PLANES 124 

Pawn  vs.  Pawn 124-127 

Pawn  vs.  Knight 128 

Knight  vs.  Knight 129 

Bishop  vs.  Pawn 13° 

Bishop  vs.  Knight      .     .     .    _. 131-133 

Rook  y5.  Pawn i34 

Rook  vs.  Knight 135-137 

Queen  vs.  Pawn 138 

Queen  vs.  Knight 139-142 

King  vs.  Pawn 143 


Xll  CONTENTS. 

SIMPLE  TACTICAL  PLANES  (continued). 

King  vs.  Knight 144 

Two  Pawns  vs.  Knight 145 

Two  Pawns  vs.  Bishop 146 

Pawn  and  Knight  vs.  Knight 147 

Pawn  and  Knight  vs.  Bishop 148 

Pawn  and  Bishop  vs.  Bishop 149 

Pawn  and  Rook  vs.  Rook ..150 

Two  Knights  vs.  Knight 151 

Knight  and  Bishop  vs.  Knight 152 

Knight  and  Rook  vs.  Knight 153 

Knight  and  Queen  vs.  Knight 154 

Knight  and  King  vs.  Knight 155 

Bishop  and  Queen  vs.  Knight 156 

Rook  and  Queen  vs.  Knight 157 

King  and  Queen  vs.  Knight 158 

COMPOUND  TACTICAL  PLANES 159 

Pawn  vs.  Two  Knights 159 

Knight  vs.  Rook  and  Bishop 160 

Knight  vs.  King  and  Queen 161 

Bishop  vs.  Two  Pawns 162 

Bishop  vs.  King  and  Pawn 163 

Bishop  vs.  King  and  Knight 164 

Bishop  vs.  Two  Knights 165 

Bishop  vs.  King  and  Knight 166 

Rook  vs.  Two  Knights 167 

Rook  vs.  Knight  and  Bishop 168,  169 

Queen  vs.  Knight  and  Bishop 170,171 

Queen  us.  Knight  and  Rook 172 

Queen  us.  Bishop  and  Rook 173 

King  vs.  Knight  and  Pawn 1 74 

King  vs.  Bishop  and  Pawn 1 75 

King  vs.  King  and  Pawn 176 

Knight  vs.  Three  Pawns 177 

Bishop  vs.  Three  Pawns 178 

Rook  vs.  Three  Pawns 179 

King  vs.  Three  Pawns 180 

Knight  vs.  Bishop  and  Pawn 181 

Bishop  vs.  Bishop  and  Pawn 187 


CONTENTS.  xiii 

PAGE 

COMPLEX  TACTICAL  PLANES 183 

Knight  and  Pawn  vs.  King  and  Queen       .....  183,  184 

Bishop  and  Pawn  vs.  King  and  Queen 185 

Bishop  and  Knight  vs.  King  and  Queen 186-192 

Rook  and  Knight  vs.  King  and  Queen 193-195 

Queen  and  Bishop  vs.  King  and  Queen 196 

Queen  and  Rook  vs.  King  and  Queen 197 

Bishop  and  Pawn  vs.  King  and  Knight 198 

Bishop  and  Pawn  vs.  King  and  Bishoj        199 

Bishop  and  Pawn  vs.  Knight  and  Bishop 200 

Bishop  and  Pawn  vs.  Knight  and  Rook 201 

Bishop  and  Pawn  vs.  King  and  Queen 202 

Rook  and  Pawn  vs.  King  and  Bishop 203 

Rook  and  Pawn  us.  King  and  Rook 204 

Rook  and  Pawn  vs.  King  and  Queen 205 

Queen  and  Pawn  vs.  Rook  and  Bishop 206 

Queen  and  Pawn  vs.  Rook  and  Knight 207 

Queen  and  Pawn  vs.  Bishop  and  Knight 208 

King  and  Pawn  vs.  Bishop  and  Knight 209 

King  and  Pawn  vs.  Two  Knights 210 

SIMPLE  LOGISTIC  PLANES 211 

Pawn  vs.  Pawn 211-213 

Pawn  us.  Knight 214 

Pawn  vs.  Bishop 215 

Pawn  vs.  King 216 

Knight  and  Pawn  vs.  Queen  or  Rook 217 

Bishop  and  Pawn  vs.  King  and  Rook 218 

Rook  and  Pawn  vs.  Rook 219 

Knight  and  Pawn  vs.  King 220 

Rook  and  Pawn  vs.  King 221 

Bishop  and  Pawn  us.  King  and  Queen 222 

COMPOUND  LOGISTIC  PLANES 223 

Two  Pawns  vs.  Pawn 223,  224 

Two  Pawns  us.  Knight 225,  226 

Two  Pawns  us.  Bishop 227,  228 

Two  Pawns  us.  Rook 229 

Two  Pawns  iw.  Kins  230,  231 


xiv  CONTENTS. 

PAGE 

COMPLEX  LOGISTIC  PLANES 23-2 

Three  Pawns  vs.  Three  Pawns     .........232 

Three  Pawns  vs.  King 233 

Three  Pawns  vs.  Queen 234 

Three  Pawns  vs.  King  and  Pawn 235 

JSIMPLE  STRATEGIC  PLANES 236 

Knight  vs.  Objective  Plane  1       236 

Knight  vs.  Objective  Plane  2 237 

Bishop  vs.  Objective  Plane  2        ...     238 

Bishop  vs.  Objective  Plane  3 239 

Rook  vs.  Objective  Plane  2 240 

Rook  vs.  Objective  Plane  3 241 

Queen  vs.  Objective  Plane  2 242,  243 

Queen  vs.  Objective  Plane  3 244,  245 

Queen  vs.  Objective  Plane  4 246 

COMPOUND  STRATEGIC  PLANES 247 

Pawn  and  S.  F.  vs.  Objective  Plane  2 247 

Bishop  and  S.  F.  vs.  Objective  Plane  3 248,  249 

Rook  and  S.  F.  vs.  Objective  Plane  3 250 

Rook  and  S.  F.  vs.  Objective  Plane  4 251 

Rook  and  S.  F.  vs.  Objective  Plane  5 252 

Queen  and  S.  F.  vs.  Objective  Plane  7 253,  254 

COMPLEX  STRATEGIC  PLANES 255 

Pawn  Lodgment  vs.  Objective  Plane  8 255 

Knight  Lodgment  vs.  Objective  Plane  8 256 

Bishop  Lodgment  rs.  Objective  Plane  8 257 

Rook  Lodgment  vs.  Objective  Plane  8        258 

Pawn  Lodgment  vs.  Objective  Plane  9 259 

Bishop  Lodgment  vs.  Objective  Plane  9 260,  261 

Rook  Lodgment  vs.  Objective  Plane  9        262 

Vertical  Pieces  vs.  Objective  Plane  9 263 

Oblique  et  al.  Pieces  vs.  Objective  Plane  9 263 

Diagonal  Pieces  vs.  Objective  Plane  9 264 

Horizontal  Pieces  vs.  Objective  Plane  9 265 

LOGISTICS  OF  GEOMETRIC  PLANES  ....    266 


INTEODUCTORY. 


WHEN  you  walked  into  your  office  this  morning, 
you  may  have  noticed  that  your  senior  partner 
was  even  more  than  ordinarily  out  of  sorts,  which,  of 
course,  is  saying  a  good  deal. 

In  fact,  the  prevailing  condition  in  his  vicinity  was  so 
perturbed  that,  without  even  waiting  for  a  response, 
say  nothing  of  getting  any,  to  your  very  civil  salutation, 
you  picked  up  your  green  bag  again  and  went  into  court ; 
leaving  the  old  legal  luminary,  with  his  head  drawn 
down  between  his  shoulders  like  a  big  sea-turtle,  to 
glower  at  the  wall  and  fight  it  out  with  himself. 

Furthermore,  you  may  recollect,  it  was  in  striking 
contrast  that  his  Honor  blandly  regarded  your  arrival, 
and  that  it  was  with  an  emphasized  but  strictly  judicial 
snicker  that  he  inquired  after  the  health  of  your  vener- 
able associate. 

You  replied  in  due  form,  of  course,  but  being  a  bit 
irritated,  as  is  natural,  you  did  not  hesitate  to  insin- 
uate that  some  kind  of  a  blight  seemed  to  have  struck 
in  your  partner's  neighborhood  during  the  night ;  where- 
upon you  were  astonished  to  see  the  judge  tie  himself  up 
into  a  knot,  and  then  with  face  like  an  owl  stare  straight 
before  him,  while  the  rest  of  his  anatomy  acted  as  if  it 
had  the  colic. 

Were  you  a  chess-player,  you  would  understand  all 
this  very  easily.  But  as  you  do  not  practise  the  game, 


xvi  INTRODUCTORY. 

and  this  is  the  first  book  you  ever  read  on  the  subject,  it 
is  necessary  to  inform  you  that  your  eminent  partner 
and  the  judge  had  a  sitting  at  chess  last  night,  and  there 
is  reason  to  believe  that  your  alter  ego  did  not  get  all  the 
satisfaction  out  of  it  that  he  expected. 

You  have  probably  heard  of  that  far-away  country 
whose  chief  characteristics  are  lack  of  water  and  good 
society,  and  whose  population  is  afflicted  with  an  uncon- 
trollable chagrin.  These  people  have  their  duplicates 
on  earth,  and  your  partner,  about  this  time,  is  one  of 
them. 

Therefore,  while  you  are  attending  strictly  to  business 
and  doing  your  prettiest  to  uphold  the  dignity  of  your 
firm,  it  may  interest  you  to  know  what  the  eminent  head 
of  your  law  concern  is  doing.  Not  being  a  chess-player, 
you  of  course  assume  that  he  is  still  sitting  in  a  pro- 
found reverie,  racking  his  brains  on  some  project  to 
make  more  fame  and  more  money  for  you  both. 

But  he  is  doing  nothing  of  the  kind.  As  a  matter  of 
fact,  he  still  is  sitting  where  you  left  him,  morose  and 
ugly,  and  engaged  in  frescoing  the  wainscoting  with  the 
nails  in  his  bootheels.  Yet  nothing  is  further  from  his 
mind  than  such  low  dross  as  money  and  such  a  perish- 
able bauble  as  fame.  At  this  moment  he  has  but  a 
single  object  in  life,  and  that  is  to  concoct  some  Mach- 
iavellian scheme  by  which  to  paralyze  the  judge  when 
they  get  together  this  evening.  This,  by  the  way,  they 
have  a  solemn  compact  to  do. 

Thus  your  partner  is  out  of  sorts,  and  with  reason. 
To  be  beaten  by  the  judge,  who  (as  your  partner  will 
tell  you  confidentially)  never  wins  a  game  except  by 
purest  bull  luck,  is  bad  enough.  Still,  your  partner, 
buoyed  up  by  the  dictates  of  philosophy  and  the  near 
prospect  of  revenge,  —  a  revenge  the  very  anticipation  of 


INTRODUCTORY.  xvil 

which  makes  his  mouth  water,  —  could  sustain  even  that 
load  of  ignominy  for  at  least  twenty-four  hours.  But 
what  has  turned  loose  the  flood-gates  of  his  bile  is  that 
lot  of  books  on  the  floor  beside  him.  You  saw  these  and 
thought  they  were  law  books ;  but  they  're  not,  they  are 
analytical  treatises  on  chess,  which  are  all  right  if  your 
opponent  makes  the  moves  that  are  laid  down  for  him 
to  make,  and  all  wrong  if  he  does  not.  Your  partner 
knows  that  these  books  are  of  no  use  to  him,  for  the 
judge  does  n't  know  a  line  in  any  chess-book,  and  prides 
himself  on  the  fact. 

It  seems  that  the  judge,  when  he  plays  chess,  prefers 
to  use  his  brains,  and  having  of  these  a  fair  supply  and 
some  conception  of  common-sense  and  of  simple  arith- 
metic, he  has  the  habit,  a  la  Morphy,  of  making  but  one 
move  at  a  time,  and  of  paying  particular  attention  to 
its  quality. 

Thus,  in  order  to  beat  the  judge  to-night,  your  partner 
realizes  that  he  must  get  down  to  first  principles  in  the 
art  of  checkmating  the  adverse  king,  of  queening  his 
own  pawns,  and  of  capturing  hostile  pieces.  But  in 
the  analytical  volumes  which  he  has  been  strewing 
about  the  floor  he  can  find  nothing  about  first  prin- 
ciples, or  about  principles  of  any  kind  for  that  matter. 
This  makes  your  partner  irritable,  for  he  is  one  of  those 
men  who,  when  they  want  a  thing,  want  it  badly  and 
want  it  quick.  So  if  you  are  through  with  this  book 
you  had  better  send  it  over  to  him  by  a  boy. 


MAJOR  TACTICS. 


MAJOR   TACTICS. 


MAJOR  TACTICS  is  that  branch  of  the  science  of 
chess  strategetics  which  treats  of  the  evolutions 
appertaining  to  any  given  integer  of  chess  force  when 
acting  either  alone,  or  in  co-operation  with  a  kindred 
integer,  against  any  adverse  integer  of  chess  force ;  the 
latter  acting  alone,  or,  in  combination  with  any  of  its 
kindred  integers. 

An  Evolution  is  that  combination  of  the  primary 
elements  —  time,  locality  and  force  —  whereby  is  made 
a  numerical  gain ;  either  by  the  reduction  of  the  ad- 
verse material,  or  by  the  augmentation  of  the  kindred 
body  of  chess-pieces. 

In  every  evolution,  the  primary  elements  time, 
locality  and  force  —  are  determinate  and  the  proposi- 
tion always  may  be  mathematically  demonstrated. 

The  object  of  an  evolution  always  is  either  to  check- 
mate the  adverse  king ;  or,  to  capture  an  adverse  pawn 
or  piece ;  or  to  promote  a  kindred  pawn. 

Grand  Law  of  Major  Tactics.  —  The  offensive  force  of  a 
given  piece  is  valid  at  any  point  against  which  it  is 
directed  ;  but  the  defensive  force  of  a  given  piece  is 
valid  for  the  support  only  of  one  point,  except  when 
the  points  required  to  be  defended  are  all  contained  in 
the  perimeter  of  that  geometric  figure  which  appertains 
to  the  supporting  piece. 


GEOMETRIC  SYMBOLS. 

All  integers  of  chess  force  are  divided  into  six 
classes  ;  the  King,  the  Queen,  the  Rook,  the  Bishop,  the 
Knight  and  the  Pawn. 

Any  one  of  these  integers  may  properly  be  combined 
with  any  other  and  the  principle  upon  which  such  com- 
bination is  based  governs  all  positions  in  which  such 
integers  are  combined.  "This  principle  always  assumes 
a  form  similar  to  a  geometric  theorem  and  is  susceptible 
of  exact  -demonstration. 

That  geometric  symbol  which  is  the  prime  factor  in 
all  evolutions  which  contemplates  the  action  of  a  Pawn 
is  shown  in  Fig.  1. 

This  figure  is  an  inverted  triangle,  whose  base  always 
is  coincident  with  one  of  the  horizontals  of  the  chess- 
board; whose  sides  are  diagonals  and  whose  verux 
always  is  that  point  which  is  occupied  by  the  given 
pawn. 


GEOMETRIC  SYMBOLS. 


GEOMETRIC  SYMBOL  OF  THE  PAWN. 
FIGURE  l. 

Black. 


White. 


PRINCIPLE. 


Given  a  Pawn's  triangle,  the  vertices  of  which  are 
occupied  by  one  or  more  adverse  pieces,  then  the  pawn 
may  make  a  gain  in  adverse  material. 


MAJOR  TACTICS. 


That  geometric  symbol  which  is  the  prime  factor  in 
all  evolutions  that  contemplate  the  action  of  a  Knight  is 
shown  in  Fig.  2. 

This  figure  is  an  octagon,  the  centre  of  which  is  the 
point  occupied  by  the  Knight  and  whose  vertices  are  the 
extremities  of  the  obliques  which  radiate  from  the  given 
centre. 

GEOMETRIC  SYMBOL  OF  THE  KNIGHT. 
FIGURE  2. 

Black. 


White. 
PRINCIPLE. 


Given  a  Knight's  octagon,  the  vertices  of  which  are 
occupied  by  one  or  more  adverse  pieces,  then  the  Knight 
may  make  a  gain  in  adverse  material. 


GEOMETRIC  SYMBOLS.  ,  7 

The  geometric  symbol  which  is  the  prime  factor  in  all 
evolutions  which  contemplate  the  action  ef  a  Bishop  is 
shown  in  Fig.  3. 

This  figure  is  a  triangle,  the  vertex  of  which  always 
is  that  point  which  is  occupied  by  the  Bishop. 


GEOMETRIC  SYMBOL  OF  THE  BISHOP. 

FIGURE  3. 

Black. 


White. 


PRINCIPLE. 

Given  a  Bishop's  triangle,  the  vertices  of  which  are 
occupied  by  one  or  more  adverse  pieces,  then  the  Bishop 
mav  make  a  gain  in  adverse  material. 


8 


MAJOR   TACTICS 


That  geometric  symbol  which  is  a  prime  factor  in 
all  evolutions  which  contemplate  the  action  of  a  Rook 
is  shown  in  Fig.  4. 

This  figure  is  a  quadrilateral,  one  angle  of  which  is 
the  point  occupied  by  the  Rook. 

GEOMETRIC  SYMBOL  OF  THE  BOOK. 

FIGURE  4. 
Black. 


While. 


PRINCIPLE. 

Given  a  Rook's  quadrilateral,  one  of  whose  sides  is 
occupied  by  two  or  more  adverse  pieces ;  or  two  or  more 
of  whose  sides  are  occupied  by  one  or  more  adverse 
pieces ;  then  the  Rook  may  make  a  gain  in  adverse 
material. 


GEOMETRIC  SYMBOLS. 


9 


That  geometric  symbol  which  is  a  prime  factor  in  all 
evolutions  that  contemplate  the  action  of  the  Queen  is 
shown  in  Fig.  5. 

This  figure  is  an  irregular  polygon  of  which  the  Queen 
occupies  the  common  vertex. 

GEOMETRIC  SYMBOL  OF  THE  QUEEN. 
FIGURE  5. 

Black. 


White. 


NOTE.  — This  figure   is  composed  of  a  rectangle,  a 
minor  triangle,  a  major  triangle,  and  a  quadrilateral,  and 
shows  that  the  Queen  combines  the  offensive  powers 
of  the  Pawn,  the  Bishop,  the  Rook  and  the  King. 
PRINCIPLE. 

Given  one  or  more  adverse  pieces  situated  at  the 
vertices  or  on  the  sides  of  a  Queen's  polygon,  then 
the  Queen  may  make  a  gain  in  adverse  material. 


10 


MAJOR   TACTICS. 


That  geometric  symbol  which  is  the  prime  factor  in 
all  evolutions  which  contemplate  the  action  of  the  King, 
is  shown  in  Fig.  6. 

This  figure  is  a  rectangle  of  either  four,  six,  or 
nine  squares.  In  the  first  case  the  King  always  is 
situated  at  one  of  the  angles  ;  in  the  second  case  he 
always  is  situated  on  one  of  the  sides  and  in  the  last 
case  he  always  is  situated  in  the  centre  of  the  given 
figure. 

GEOMETRIC  SYMBOL  OF  THE  KING. 

(a.) 
FIGURE  6. 


Slack. 


White. 


PRINCIPLE. 

Given  one  or  more  adverse  pieces  situated  on  the 
sides  of  a  King's  rectangle,  then  the  King  may  make  a 
gain  in  adverse  material. 


GEOMETRIC  SYMBOLS. 


11 


A  Sub-G-eometric  Symbol  is  that  mathematical  figure 
which  in  a  given  situation  appertains  to  the  Prime 
Tactical  Factor,  and  whose  centre  is  unoccupied  by  a 
kindred  piece,  and  whose  periphery  is  occupied  by  the 
given  Prime  Tactical  Factor. 


SUB-GEOMETRIC  SYMBOL  OF  THE  PAWN. 
FIGURE  7. 


White. 


NOTE.  —  That  point  which  is  the  centre  of  the  geo- 
metric symbol  of  a  piece  always  is  the  centre  of  its 
sub-geometric  symbol. 


12 


MAJOR  TACTICS. 


SUB-GEOMETRIC   SYMBOL  OF  THE  PAWN. 

FIGURE  8. 

(b.) 

Black. 


White. 


NOTE.  —  A  piece  always  may  reach  the  centre  of  its 
sub-geometric  symbol  in  one  move. 


GEOMETRIC  SYMBOLS. 


13 


SUB-GEOMETRIC   SYMBOL  OF  THE   KNIGHT. 
FIGURE  9. 

Black. 


White. 


NOTE.  —  If  the  piece  has  the  move,  the  sub-geometric 
symbol  is  positive  ;  otherwise,  it  is  negative. 


14 


MAJOR  TACTICS. 


SUB-GEOMETRIC  SYMBOL  OF  THE  BISHOP. 
FIGURE  10. 

Black. 


White. 


NOTE.  —  The  sub-geometric  symbol  is  the  mathe- 
matical figure  common  to  situations  in  which  the  de- 
cisive blow  is  preparing. 


GEOMETRIC  SYMBOLS. 


15 


SUB-GEOMETRIC  SYMBOL  OF  THE  ROOK. 

FIGURE  11. 

Black. 


White. 


NOTE.  —  The  sub- geometric   symbol   properly  should 
eventuate  into  the  geometric  symbol. 


16 


MAJOR  TACTICS. 


SUB-GEOMETRIC  SYMBOL  OF  THE  QUEEN. 

FIGURE  12. 

Black. 


White. 


NOTE.  —  A  piece  always  moves  to  the  centre  of  its 
sub-geometric  symbol. 


GEOMETRIC  SYMBOLS. 


17 


SUB-GEOMETRIC  SYMBOL  OF  THE  KING. 
FIGURE  13. 

Black. 


White. 


NOTE.  —  An  evolution  based  upon  a  sub-geometric 
symbol  always  contemplates,  as  the  decisive  stroke,  the 
move  which  makes  the  sub-geometric  symbol  positive. 


LOGISTIC   SYMBOLS. 


The  Logistic  Symbol  of  an  integer  of  chess  force 
typifies  its  movement  over  the  surface  of  the  chess- 
board and  always  is  combined  with  the  geometric 
symbol  or  with  the  sub-geometric  symbol  in  the  execu- 
tion of  a  given  calculation. 

LOGISTIC  SYMBOL  OF  THE  PAWN. 

FIGURE  14. 

Slack. 


White. 


NOTE.  —  A  piece  moves  only  in  the  direction  of  and 
to  the  limit  of  its  logistic  radii. 


LOGISTIC  SYMBOLS. 


19 


LOGISTIC  SYMBOL  OF  THE  KNIGHT. 

FIGURE  15. 

Black. 


White. 


NOTE.  —  A  piece  having  the  move  can  proceed  at  the 
given  time  along  only  one  of  its  logistic  radii. 


20 


MAJOR   TACTICS. 


LOGISTIC  SYMBOL  OF  THE  BISHOP. 
FIGURE  16. 

Black. 


White. 


NOTE.  —  The  logistic  radii  of  a  piece  all  unite  at  the 
centre  of  its  geometric  symbol. 


LOGISTIC  SYMBOLS. 


21 


LOGISTIC  SYMBOL  OF  THE  ROOK. 
FIGURE  17. 

Black. 


White. 


NOTE.  —  The  termini  of  the  logistic  radii  of  a  piece 
always  are  the  vertices  of  its  geometric  symbol. 


22 


MAJOR   TACTICS. 


LOGISTIC  SYMBOL  OF  THE   QUEEN. 
FIGURE  18. 

Black. 


White. 


NOTE.  —  The  logistic  radii  of  a  piece  always  extend 
from  the  centre  of  its  geometric  symbol  to  the  perimeter. 


LOGISTIC  SYMBOLS. 


23 


LOGISTIC  SYMBOL  OF  THE  KING. 
FIGURE  19. 

Black. 


White. 


NOTE.  —  The  logistic  radii  of  a  piece  always  are 
straight  lines,  and  always  take  the  form  of  verticals, 
horizontals,  diagonals,  or  obliques. 


GEOMETRIC  PLANES. 

Whenever  the  geometric  symbols  appertaining  to  one 
or  more  kindred  pieces  and  to  one  or  more  adverse 
pieces  are  combined  in  the  same  evolution ;  then  that 
part  of  the  surface  of  the  chessboard  upon  which  such 
evolution  is  executed  is  termed  in  this  theory  a  G-eo' 
metric  Plane. 

Geometric  Planes  are  divided  into  three  classes : 

I.   STRATEGIC. 
II.  TACTICAL. 
III.  LOGISTIC. 

Whenever  the  object  of  a  given  evolution  is  to  gain 
adverse  material,  then  that  mathematical  figure  pro- 
duced by  the  combination  of  the  geometric  symbols 
appertaining  to  the  integers  of  chess  force  thus  engaged 
is  termed  a  Tactical  Plane. 


GEOMETRIC  PLANES. 


25 


A  TACTICAL  PLANE. 
FIGURE  20. 

Black. 


White. 


White  to  play  and  win  adverse  material. 

NOTE.  —  White  having  the  move,  wins  by  1  P  —  K  6 
(ck)  followed  by  2  Kt-K  Kt  5  (ck)  if  Black  plays 
1  QxP;  and  by  2  Kt  — Q  B  5  (ck)  if  Black  plays 
IKxP. 


26 


MAJOR  TACTICS. 


Whenever  the  object  of  a  given  evolution  is  to  queen 
a  kindred  pawn,  then  that  mathematical  figure  pro- 
duced by  the  combination  of  the  geometric  symbols 
appertaining  to  the  integers  of  chess  force  thus  en- 
gaged is  termed  a  Logistic  Plane. 


A  LOGISTIC  PLANE. 

FIGURE  21. 
Slack. 


White. 


White  to  play  and  queen  a  kindred  pawn. 

NOTE. — White  having  the  move  wins  by  1  P  — Q  6, 
followed  by  2  P  -  Q  B  6,  if  Black  plays  1  K  P  x  P 
and  by  2  P  -  K  6,  if  Black  plays  1  B  P  x  P. 


GEOMETRIC  PLANES. 


27 


Whenever  the  object  of  a  given  evolution  is  to  check, 
mate  tke  adverse  king,  then  that  mathematical  figure 
produced  by  the  combination  of  the  geometric  symbols 
appertaining  to  the  integers  of  chess  force  thus  engaged 
is  termed  a  Strategic  Plane. 


A  STRATEGIC  PLANE. 
FIGURE  22. 

Black. 


White. 
White  to  play  and  checkmate  the  adverse  king. 

NOTE.  —  White  having  to  move  checkmates  the  black 
King  in  one  move  by  1  R  —  K  Kt  8  (ck). 


PLANE  TOPOGRAPHY. 

Those  verticals,  horizontals,  diagonals,  and  obliques, 
and  the  points  situated  thereon,  which  are  contained  in 
a  given  evolution,  constitute,  when  taken  collectively, 
the  Topography  of  a  given  plane. 

Every  plane,  whether  strategic,  tactical,  or  logistic, 
always  contains  the  following  topographical  features  :  — 

1.  Zone  of  Evolution.  14.  Tactical  Front. 

2.  Kindred  Integers.  15.  Front  Offensive. 

3.  Hostile  Integers.,  16.  Front  Defensive. 

4.  Prime  Tactical  Factor.  17.  Supporting  Front. 

5.  Supporting  Factor.  18.  Front  Auxiliary. 

6.  Auxiliary  Factor.  19.  Front  of  Interference. 

7.  Piece  Exposed.  20.  Point  of  Co-operation. 

8.  Disturbing  Integer.  21.  Point  of  Command. 

9.  Primary  Origin.  22.  Point  Commanded. 

10.  Supporting  Origin.  23.  Prime  Radius  of  Offence, 

11.  Auxiliary  Origin.  24.  Tactical  Objective. 

12.  Point  Material.  25.  The  Tactical  Sequence. 

13.  Point  of  Interference. 


PLANE   TOPOGRAPHY. 


29 


A  COMPLEX  TACTICAL  PLANE. 
FIGURE  23. 

Black. 


White. 
White  to  play  and  win. 

NOTE.  — White  wins  by  1  R-K  R  8  (ck),  followed, 
if  Black  plays  1  K  x  R,  by  2  Kt  -  K  B  7  (ck)  ;  and  if 
Black  plays  1  K-Kt  2,  by  2  R  x  R,  for  if  now  Black 
plays  2  Q  x  R,  then  follows  3  Kt  -K  6  (ck),  and  White 
wins  the  black  Q. 


MAJOR   TACTICS. 


A  SUB-GEOMETKIC   SYMBOL  POSITIVE. 
(G.  S.  P.) 
FIGURE  24. 

Black. 


White. 
White  to  move. 


NOTE.  —  White  having  to  move,  the  geometric  symbol 
is  positive  ;  had  Black  to  move,  the  geometric  symbol 
would  be  negative. 


PLANE   TOPOGRAPHY. 


31 


The  Zone  of  Evolution  is  composed  of  those  verticals, 
diagonals,  horizontals,  and  obliques  which  are  compre- 
hended in  the  movements  of  those  pieces  which  enter 
into  a  given  evolution.  The  principal  figure  in  any 
Zone  of  Evolution  is  that  geometric  symbol  which  ap- 
pertains to  the  Prime  Tactical  Factor. 


THE  ZONE  OF  EVOLUTION. 

(Z.  E.) 
FIGURE  25. 

Black. 


White 


NOTE.  —  The  letters  A  B  C  D  E  F  mark  the  vertices 
of  an  octagon,  which  is  the  principal  figure  in  this  evolu- 
tion, as  the  Prime  Tactical  Factor  is  a  Knight. 


32 


MAJOR   TACTICS. 


A  Kindred  Integer  is  any  co-operating  piece  which 
is  contained  in  a  given  evolution. 


KINDRED  INTEGERS. 

(K.  I.) 
FIGURE  26. 

Black. 


White, 


NOTE.  —  The  kindred  Integers  always  have  the  move 
in  any  given  evolution,  and  always  are  of  the  same  color 
-as  the  Prime  Tactical  Factor. 


PLANE   TOPOGRAPHY. 


33 


A  Hostile  Integer  is  any  adverse  piece  which  is  con- 
tained  in  a  given  evolution. 


HOSTILE  INTEGERS. 

(H.  I.) 
FIGURE  27. 

Black. 


White. 


NOTE.  —  The  Hostile  Integers  never  have  the  move 
in  any  evolution  and  always  are  opposite  in  color  to  the 
Prime  Tactical  Factor. 


34 


MAJOR  TACTICS. 


The  Prime  Tactical  Factor  is  that  kindred  Pawn  or 
Piece  which  in  a  given  evolution  either  check-mates 
the  adverse  King,  or  captures  adverse  material,  or  is 
promoted  to  and  utilized  as  some  other  kindred  piece. 


THE  PRIME  TACTICAL  FACTOR. 
(P.  T.  F.) 
FIGURE  28. 

Black. 


White. 


NOTE.  —  The  Prime  Tactical  Factor  always  is  situated 
either  at  the  centre  or  upon  the  periphery  of  the  zone  of 
evolution. 


PLANE   TOPOGRAPHY. 


35 


The  Supporting  Factor  is  that  kindred  piece  which 
directly  co-operates  in  an  evolution  with  the  Prime 
Tactical  Factor. 


THE  SUPPORTING  FACTOR. 

(S.  F.) 
FIGURE  29. 

Black. 


Wile. 


NOTE.  —  The   Supporting  Factor  always  is  situated 
upon  one  of  the  sides  of  the  zone  of  evolution. 


36 


MAJOR   TACTICS. 


An  Auxiliary  Factor  is  that  kindred  piece  which 
indirectly  co-operates  with  the  Prime  Tactical  Factor  by 
neutralizing  the  interference  of  hostile  pieces  not  con- 
tained in  the  immediate  evolution. 


AN  AUXILIARY  FACTOR. 

(A.  F.) 
FIGURE  30. 

Black. 


White. 


NOTE.  —  The  Auxiliary  Factor  may  be  situated  at 
any  point  and  either  within  or  outside  of  the  zone  of 
evolution. 


PLANE   TOPOGRAPHY. 


37 


The  Piece  Exposed  is  that  adverse  integer  of  chess 
force  whose  capture  in  a  given  evolution  may  be 
mathematically  demonstrated. 


THE  PIECE  EXPOSED. 

(P.  E.) 
FIGURE  31. 

Black. 


While. 


NOTE.  —  The  Piece  Exposed  always  is  situated  either 
upon  one  of  the  sides  or  at  one  of  the  vertices  of  the 
zone  of  evolution. 


38 


MAJOR  TACTICS. 


A  Disturbing  Integer  is  an  adverse  piece  which 
prevents  the  Prime  Tactical  Factor  from  occupying  the 
Point  of  Command,  or  the  Supporting  Factor  from 
occupying  the  Point  of  Co-operation. 


A  DISTURBING  FACTOR. 

(D.  F.) 
FIGURE  32. 

Black. 


White. 


NOTE.  —  A  Disturbing  Factor  may  or  may  not  be  situ- 
ated within  the  zone  of  evolution. 


PLANE   TOPOGRAPHY. 


39 


The  Primary  Origin  is  that  point  which,  at  the 
beginning  of  an  evolution,  is  occupied  by  the  Prime 
Tactical  Factor. 


THE  PRIMARY  ORIGIN. 

(P.  0.) 
FIGURE  33. 

Black. 


White. 


NOTE.  —  The  point  A  is  the  Primary  Origin  in  this 
evolution,  as  it  is  the  original  post  of  the  Prime  Tactical 
Factor. 


40 


MAJOR   TACTICS. 


The  Supporting  Origin  is  the  point  occupied  by  the 
Supporting  Factor  at  the  beginning  of  an  evolution. 


THE  SUPPORTING  ORIGIN. 

(P.  S.) 
FIGURE  34. 

Black. 


White. 


NOTE.  —  The  point  A  is  the  Supporting  Origin  in  this 
evolution,  as  it  is  the  original  post  of  the  Supporting 
Factor. 


PLANE   TOPOGRAPHY 


41 


The  Auxiliary   Origin  is  the   point  occupied  by  the 
Auxiliary  Factor  at  the  beginning  of  an  evolution. 


A  POINT  AUXILIARY. 

(P.  A.) 
FIGURE  35. 

Black. 


White. 


NOTE.  —  The  Point  A  is  the  Auxiliary  Origin  in  this 
evolution,  as  it  is  the  original  post  of  the  Auxiliary 
Factor. 


42 


MAJOR  TACTICS. 


The  Point  Material  is  that  point  which  is  occupied  by 
the  adverse  piece  which,  in  a  given  evolution,  it  is 
proposed  to  capture. 


POINTS  MATERIAL. 
(P.  M.) 

FIGURE  36. 

Slack. 


White. 


NOTE.  —  A  Point  Material  always  is  situated  either 
at  one  of  the  vertices  or  upon  one  of  the  sides  of  the 
zone  of  evolution. 


PLANE   TOPOGRAPHY. 


43 


A  Point  of  Interference  is  that  point  which  is  oc- 
cupied by  the  Disturbing  Integer. 


A  POINT  OF  INTERFERENCE. 

(P.  I.) 
FIGURE  37. 

Black. 


White. 


NOTE.  —  The  point  A  is  the  Point  of  Interference  in 
this  evolution,  as  it  is  the  original  post  of  the  Disturbing 
Factor. 


44 


MAJOR  TACTICS. 


The  Tactical  Front  is  composed  of  the  Fronts  Offen- 
sive, Defensive,  Auxiliary,  Supporting,  and  of  Inter- 
ference. 


THE  TACTICAL  FRONT. 

(T.  F.) 
FIGURE  38. 

Black. 


While. 

NOTE. — The  Front  Offensive  extends  from  White's 
K  Kt  5  to  K  B  7 ;  the  Front  Defensive  from  K  Kt  1  to  K 
B  2 ;  the  Front  of  Interference  from  Q  Kt  3  to  K  B  7 ; 
the  Front  Supporting  from  KR7  to  KR8;  the  Front 
Auxiliary  is  at  QB4. 


PLANE   TOPOGRAPHY. 


45 


The  Front  Offensive  is  that  vertical,  diagonal,  hori- 
zontal, or  oblique  which  connects  the  Primary  Origin 
with  the  Point  of  Command. 


THE  FRONT  OFFENSIVE. 
FIGURE  39. 
Black. 


NOTE.  —  The  Front  Offensive  extends  from  White's 
KKt5toKB7. 


46 


MAJOR   TACTICS. 


The  Front  Defensive  is  that  vertical,  horizontal,  diag- 
onal, or  oblique  which  extends  from  the  Point  of  Com- 
mand to  any  point  occupied  by  a  hostile  integer  con- 
tained in  the  geometric  symbol  which  appertains  to  the 
Prime  Tactical  Factor. 


THE  FRONT  DEFENSIVE. 

(F.  D.) 
FIGURE  40. 

Black. 


White. 


NOTE.  —  The  Front  Defensive  in  this  evolution  extends 
from  black  K  Kt  1  to  K  B  2. 


PLANE   TOPOGRAPHY. 


47 


TJie  Supporting  Front  is  that  vertical,  horizontal,  di- 
agonal, and  oblique  which  unites  the  Supporting  Origin 
with  the  Point  of  Co-operation. 


THE   SUPPORTING  FRONT. 
FIGURE  41. 

Black. 


White. 


NOTE.  —  The  Front  of  Support  in  this  evolution  ex- 
tends from  White's  K  R  7  to  K  R  8. 


MAJOR   TACTICS. 


A  Front  Auxiliary  is  that  vertical,  horizontal,  diag- 
onal, or  oblique  which  extends  from  the  Point  Auxiliary 
to  the  Point  of  Interference  ;  or  that  point  situated  on 
the  Front  of  Interference  which  is  occupied  by  the  Aux- 
iliary Factor. 

The  Front  of  Interference  is  that  vertical,  horizontal, 
diagonal,  or  oblique  which  unites  the  Point  of  Inter- 
ference with  the  Point  of  Command,  or  with  the  Point 
of  Co-operation. 

A  FRONT  OF  INTERFERENCE. 

(F.  I.) 
FIGURE  42. 

Black. 


White. 


NOTE.  —  The  Front  of  Interference  in  this  evolution 
extends  from  White's  Q  Kt  3  to  K  B  7. 


PLANE   TOPOGRAPHY. 


49 


The  Point  of  Co-operation  is  that  point  which  when 
occupied  by  the  Supporting  Factor  enables  the  Prime 
Tactical  Factor  to  occupy  the  Point  of  Command. 


THE  POINT  OF  CO-OPERATION. 
FIGURE  43. 

Black. 


White. 


NOTE.  —  The  Point  of  Co-operation  in  this  evolution 
is  the  white  square  K  R  8. 


50 


MAJOR  TACTICS. 


The  Point  of  Command  is  the  centre  of  that  geomet- 
ric symbol  which  appertains  to  the  Prime  Tactical 
Factor,  and  which,  when  occupied  by  the  latter,  wins  an 
adverse  piece,  or  checkmates  the  adverse  king,  or  en- 
sures the  queening  of  a  kindred  pawn. 


THE  POINT  OF  COMMAND. 

(P.  C.) 
FIGURE  44. 

Slack. 


White. 


NOTE.  —  The  Point  of  Command  in  this  evolution  is 
the  white  square  K  B  7. 


PLANE   TOPOGRAPHY. 


51 


The  Point  Commanded  is  that  point  at  which  the 
Piece  Exposed  is  situated  when  the  Prime  Tactical 
Factor  occupies  the  Point  of  Command. 


THE  POINT  COMMANDED. 

(C.  P.) 
FIGURE  45. 

(a.) 
Black. 


White. 


NOTE.  —  White  has  occupied  the  Point  of  Co-operation 
with  the  Supporting  Factor,  which  latter  has  been  cap- 
tured by  the  black  King,  thus  allowing  the  white  Knight 
to  occupy  the  Point  of  Command. 


52 


MAJOR   TACTICS. 


THE  POINT  COMMANDED. 

(C.  P.) 
FIGURE  46. 

(6.) 
Black. 


White. 

NOTE.  —  Black  retired  before  the  attack  of  the  Sup- 
porting Factor,  still  defending  the  Point  of  Command. 
The  Supporting  Factor  then  captured  the  black  Rook, 
thus  opening  up  a  new  and  unprotected  Point  of  Com- 
mand, which  is  occupied  by  the  white  Knight. 

Those  interested  in  military  science  may,  perhaps, 
understand  from  these  two  diagrams  why  all  the  great 
captains,  from  Tamerlane  to  Yon  Moltke,  so  strenuously 
recommended  the  study  of  chess  to  their  officers. 


PLAJSE   TOPOGRAPHY. 


53 


The  Prime  Radius  of  Offence  is  the  attacking  power 
radiated  by  the  Prime  Tactical  Factor  from  the  Point 
of  Command  against  the  Point  Commanded. 


THE  PRIME  RADIUS    OF  OFFENCE. 

(P.  R.  O.) 

FIGURE  47. 

Black. 


White. 


NOTE.  —  In  this  evolution  the  Prime  Radii  of  Offence 
extend  from  the  white  point  K  B  7  to  K  R  8,  Q  6,  and 

Q8. 


54 


MAJOR   TACTICS. 


The  Tactical  Objective  is  that  point  on  the  chess-board 
whose  proper  occupation  is  the  immediate  object  of  the 
initiative  in  any  given  evolution. 


THE  TACTICAL  OBJECTIVE. 

(T.  O.) 
FIGURE  48. 

Black. 


White. 

NOTE.  In  this  evolution  the  point  A  is  the  Tactical 
Objective,  i.e.  the  initial  movement  in  its  execution  is 
to  occupy  the  Point  of  Co-operation  with  the  Supporting 
Factor. 

The  Tactical  Sequence  is  that  series  of  moves  which 
comprehends  the  proper  execution  of  any  given 
evolution. 


TACTICAL  PLANES. 

A  Tactical  Plane  is  that  mathematical  figure  pro- 
duced by  the  combination  of  two  or  more  kindred 
geometric  symbols  in  an  evolution  whose  object  is  gain 
of  material. 

Tactical  Planes  are  divided  into  three  classes,  viz. :  — 

I.   SIMPLE. 
II.  COMPOUND. 
III.  COMPLEX. 

A  Simple  Tactical  Plane  consists  of  any  kindred  geo- 
metric symbol  combined  with  a  Point  Material. 

PRINCIPLE. 

I.  Whenever  in  a  simple  Tactical  Plane,  the  Primary 
Origin  and  the  Point  Material  are  contained  in  the  same 
side  of  that  geometric  symbol  which  appertains  to  the 
Prime    Tactical    Factor,    then   the    latter,    having  the 
move,  will  overcome  the  opposing  force. 

II.  No  evolution  in  a  simple  Tactical  Plane  is  valid 
if  the  opponent  has  the  move,  or  if  not  having  the  move, 
he  can  offer  resistance  to  the  march  of  the  Prime  Tacti- 
cal Factor  along  the  Front  Offensive. 


r>6 


MAJOR   TACTICS. 


A  SIMPLE  TACTICAL  PLANE. 
FIGURE  49. 

Black. 


White. 
White  to  play  and  win  the  adverse  Kt  in  one  move. 

NOTE. — The  decisive  point  is  that  at  which  the  geo- 
metric and  the  logistic  symbols  appertaining  to  the 
Prime  Tactical  Factor  intersect. 

A  Compound  Tactical  Plane  consists  of  any  kindred 
geometric  symbol  combined  with  two  or  more  Points 
Material. 

PRINCIPLE. 

Whenever  in  a  Compound  Tactical  Plane  the  Primary 
Origin  and  two  or  more  Points  Material  are  situated  at 


TACTICAL  PLANES. 


57 


the  vertices  of  that  geometric  symbol  which  appertains 
to  the  Prime  Tactical  Factor,  then,  if  the  value  of  each  of 
the  Points  Material  exceeds  the  value  of  the  Prime  Tacti- 
cal Factor  ;  or,  if  neither  of  the  Pieces  Exposed  can  sup- 
port the  other  in  one  move,  —  the  Prime  Tactical  Factor, 
having  the  move,  will  overcome  the  opposing  force. 

II.  No  evolution  in  a  Compound  Tactical  Plane  is 
valid  if  the  opponent  can  offer  resistance  to  the  Prime 
Tactical  Factor. 


A  COMPOUND  TACTICAL  PLANE. 
FIGURE  50. 

Black. 


While. 


NOTE.  —  The  decisive  point  is  the  centre  of  the  geo- 
metric symbol  which  appertains  to  the  Prime  Tactical 
Factor. 


58  MAJtjtft*  TACTICS. 

A  Complex  Tactical  Plane  consists  of  the  combination 
of  any  two  or  more  kindred  geometric  symbols  with  one 
or  more  Points  Material. 

PRINCIPLE. 

I.  No  evolution  in  a  Complex  Tactical  Plane  is  valid 
unless  it  simplifies  the  position,  either  by  reducing  it  to 
a  Compound  Tactical  Plane  in  which  the  opponent,  even 
with  the  move,  can  offer  no  resistance  ;  or  to  a  Simple 
Tactical  Plane,  in  which  the  opponent  has  not  the  move 
nor  can  offer  any  resistance. 

II.  To  reduce  a  Complex  Tactical  Plane  to  a  Com- 
pound Tactical  Plane,  establish  the  Supporting  Origin 
at  such  a  point  and  at  such  a  time  that,  whether  the 
Supporting   Factor   be   captured   or   not,  the   Primary 
Origin  and  two  or  more  of   the  Points   Material  will 
become  situated  on  that  side  of  the  geometric  figure 
which   appertains   to    the   Prime   Tactical   Factor,  the 
latter  having  to  move. 

III.  To  reduce  a  Complex  Tactical  Plane  to  a  Simple 
Tactical  Plane,  eliminate  all  the  Points  Material  save 
one,  and  all  the  Hostile  Integers  save  one,  and  establish 
the  Primary  Origin  and  the  Point  Material  upon  the 
same  side  of  that  geometric  figure  which  appertains  to 
the  Prime  Tactical  Factor,  the  latter  having  to  move. 


TACTICAL  PLANES. 


59 


A    COMPLEX  TACTICAL  PLANE. 
FIGURE  51. 

Black. 


White. 


NOTE.  — This  diagram  is  elaborated  to  show  the  student 
the  Supplementary  Knight's  Octagon  and  the  Supple- 
mentary Point  of  Command  at  White's  K  6. 


LOGISTIC  PLANES. 

A  LOGISTIC  PLANE  is  that  mathematical  figure  pro- 
duced by  the  combination  of  two  or  more  kindred  geo- 
metric symbols  in  an  evolution  whose  object  is  to  queen 
a  kindred  pawn. 

A  LOGISTIC  PLANE  is  composed  of  a  given  logistic 
horizon,  the  adverse  pawns,  the  adverse  pawn  altitudes, 
and  the  kindred  Points  of  Resistance. 

Logistic  Planes  are  divided  into  three  classes :  — 

I.   SIMPLE. 
II.   COMPOUND. 
III.   COMPLEX. 


LOGISTIC  PLANES. 


61 


A  simple  Logistic  Plane  consists  of  a  pawn  altitude, 
combined  adversely  with  that  geometric  figure  which 
appertains  to  either  a  P,  Kt,  B,  R,  Q,  or  K. 

In  a  plane  of  this  kind  the  pawn  always  is  the  Prime 
Tactical  Factor. 

The  following  governs  all  logistic  planes  :  — 

PRINCIPLE. 

Whenever  the  number  of  pawn  altitudes  exceeds  the 
number  of  Points  of  Resistance,  the  given  pawn  queens 
without  capture  against  any  adverse  piece. 

A  SIMPLE  LOGISTIC  PLANE. 

FIGURE  52. 

Black. 


White. 


White  to  move  and  queen  a  pawn  without  capture  by  an  adverse 
piece. 


62 


MAJOR  TACTICS. 


A  Compound  Logistic  Plane  is  composed  of  two  kin- 
dred pawn  altitudes  combined  adversely  with  the  geo- 
metric figures  appertaining  to  one  or  more  opposing 
integers  of  chess  force. 


A  COMPOUND  LOGISTIC  PLANE. 
FIGURE  53. 

Black. 


White. 


White  to  move  and  queen  a  pawn  without  capture  by  the  adverse 
King. 

NOTE.  —  It  will  be  easily  seen  that  the  black  King 
cannot  stop  both  of  the  white  Pawns. 


LOGISTIC  PLANES. 


63 


A  Complex  Logistic  Plane  consists  of  three  kindred 
pawn  altitudes  combined  adversely  with  the  geometric 
figures  appertaining  to  one  or  more  opposing  integers 
of  chess  force. 


A  COMPLEX  LOGISTIC  PLANE. 
FIGURE  64. 

Black. 


White. 


White  to  move  and  queen  a  pawn  without  capture  by  the  adverse 
pieces. 

NOTE. — The  black  King  and  the  black   Bishop   are 
each  unable  to  stop  more  than  one  Pawn. 


64  MAJOR   TACTICS. 

Plane  Topography.  —  The  following  topographical 
features  are  peculiar  to  Logistic  Planes :  - 

1.  Logistic  Horizon. 

2.  Pawn  Altitude. 

3.  Point  of  Junction. 

4.  Square  of  Progression. 

5.  Corresponding  Knights  Octagon. 

6.  Point  of  Resistance. 

The  Logistic  Horizon  is  that  extremity  of  the  chess- 
board, at  which,  upon  arrival,  a  pawn  may  be  promoted 
to  the  rank  of  any  kindred  piece.  The  Logistic  Horizon 
of  White  always  is  the  eighth  horizontal ;  that  of  Black 
always  is  the  first  horizontal. 


LOGISTIC  PLANES. 


65 


THE  LOGISTIC  HORIZON. 

(White). 
FIGURE  55. 

Black. 


White. 


NOTE.  —  The  Points  of  Junction  are   designated  by 
black  dots. 


66 


MAJOR  TACTICS. 


THE  LOGISTIC  HORIZON. 
(Black.) 

FIGURE  56. 

Black. 


White. 


LOGISTIC  PLANES, 


67 


A  Pawn  Altitude  is  composed  of  those  verticals  and 
diagonals  along  which  it  is  possible  for  a  pawn  to 
pass  to  its  logistic  horizon. 


A  PAWN  ALTITUDE 

(P.  A.) 
FIGURE  57. 

Black. 


White. 


68 


MAJOR   TACTICS. 


A  Point  of  Junction  is  that  point  at  which  an  extremity 
of  a  pawn  altitude  intersects  the  logistic  horizon,  i.  e.  the 
queening  point  of  a  given  pawn. 


A  POINT  OF  JUNCTION. 

(P.  J.) 
FIGURE  58. 

Black. 


White. 


LOGISTIC  PLANES. 


69 


The  Square  of  Progression  is  that  part  of  the  logistic 
Plane  of  which  the  pawn's  vertical  is  one  side  and  whose 
area  is  the  square  of  the  pawn's  altitude. 


A  SQUARE  OF  PROGRESSION. 

(S.  P.) 
FIGURE  59. 

Black. 


White. 


70 


MAJOR   TACTICS. 


The  Corresponding  Knight's  Octagon  is  that  Knight 
octagon  whose  centre  is  the  queening  point  of  the  pawn, 
and  whose  radius  consists  of  a  number  of  Knight's  moves 
equal  to  the  number  of  moves  to  be  made  by  the  pawn 
in  reaching  its  queening  point. 


THE  CORRESPONDING  KNIGHT'S  OCTAGON. 
(C.  K.  0.) 

FIGURE  60. 
Black. 


White. 


NOTE.  —  The  pawn  has  but  two  moves  to  make  in  order 
to  queen.  The  points  ABODE  are  two  Knight's  moves 
from  the  queening  point. 


LOGISTIC  PLANES. 


71 


A  Point  of  Resistance  is  that  point  on  a  pawn  altitude 
which  is  commanded  by  a  hostile  integer  and  which  is 
situated  between  the  Primary  Origin  and  the  Point  of 
Junction. 


POINT  OF  RESISTANCE. 
(P.  R.) 

FIGURE  61. 
fcfaafc 


White. 


NOTE.  —  In  this  evolution,  the  points  A  and  B  are 
points  of  resistance,  as  they  prevent  the  queening  of  the 
Prime  Tactical  Factor. 


STRATEGIC   PLANES. 

A  STRATEGIC  PLANE  is  that  mathematical  figure  pro- 
duced by  the  combination  of  two  or  more  geometric 
symbols  in  an  evolution  whose  object  is  to  checkmate 
the  adverse  King. 

A  STRATEGIC  PLANE  is  composed  of  a  given  Objective 
Plane  and  of  the  Origins  occupied  by  the  attacking  and 
by  the  defending  pieces. 

Strategic  planes  are  divided  into  three  classes :  — 

I.   SIMPLE. 
II.  COMPOUND. 
III.  COMPLEX. 


STRATEGIC  PLANES. 


73 


A  Simple  Strategic  Plane  is  one  which  may  be  com- 
manded by  the  Prime  Tactical  Factor. 

Simple  Strategic  Planes  are  governed  by  the  follow- 
ing 

PRINCIPLE. 

Whenever  the  net  value  of  the  offensive  force  radiated 
by  a  given  piece  is  equal  to  the  net  mobility  of  the 
Objective  Plane ;  then,  the  given  piece  may  checkmate 
the  adverse  King. 


A  SIMPLE  STRATEGIC  PLANE. 
FIGURE  62. 

Black. 


White. 
White  to  play  and  mate  in  one  move. 


74 


MAJOR  TACTICS. 


A  Compound  Strategic  Plane  is  one  which  may  be 
commanded  by  the  Prime  Tactical  Factor  with  the  aid 
of  either  the  supporting  or  the  auxiliary  Factor. 

Compound  Strategic  Planes  are  governed  by  the 
following 

PRINCIPLE. 

Whenever  the  net  value  of  the  offensive  force  radiated 
by  two  kindred  pieces  is  equal  to  the  net  mobility  of  the 
Objective  Plane,  then  the  given  pieces  may  checkmate 
the  adverse  King. 

A  COMPOUND  STRATEGIC  PLANE. 

(a.) 
FIGURE  63. 

Slack. 


While. 
White  to  play  and  mate  in  one  move. 


STRATEGIC  PLANES. 


75 


A  COMPOUND  STRAGETIC  PLANE. 


FIGURE  64. 

Black. 


Whitf. 

White  to  play  and  mate  in  one  move. 


76 


MAJOR   TACTICS. 


A  Complex  Strategic  Plane  is  one  that  can  be  com- 
manded by  the  Prime  Tactical  Factor  only  when  aided 
by  both  the  supporting  and  the  Auxiliary  Factors. 

Complex  Strategic  Planes  are  governed  by  the  follow- 
ing 

PRINCIPLE. 

Whenever  the  net  value  of  the  offensive  force  radiated 
by  three  or  more  kindred  pieces  is  equal  to  the  net 
mobility  of  the  Objective  Plane,  then  the  given  kindred 
pieces  may  checkmate  the  adverse  King. 

A  COMPLEX  STRATEGIC  PLANE. 
FIGURE  65. 

Slack. 


White. 
White  to  play  and  mate  in  one  move. 


STRATEGIC  PLANES.  7? 


PLANE   TOPOGRAPHY. 

The  following  topographical  features  are  peculiar  to 
Strategic  Planes :  — 

1.  Objective  Plane. 

2.  Objective  Plane  Commanded. 

3.  Point  of  Lodgment. 

4.  Point  of  Impenetrability. 

5.  Like  Point. 

6.  Unlike  Point. 


78 


MAJOR  TACTICS. 


The  Objective  Plane  is  composed  of  the  point  oc- 
cupied by  the  adverse  King,  together  with  the  imme- 
diately adjacent  points. 


THE  OBJECTIVE  PLANE. 
FIGURE  66. 

Black. 


White. 


NOTE.  —  The  Objective  Plane  is  commanded  when  it 
contains  no  point  open  to  occupation  by  the  adverse 
King,  by  reason  of  the  radii  of  offence  operated  against 
it  by  hostile  pieces. 


STRATEGIC  PLANES. 


79 


AN  OBJECTIVE  PLANE  COMMANDED. 

FIGURE  67. 

Black. 


White. 


80 


MAJOR   TACTICS. 


A  Point  of  Lodgment  is  a  term  used  to  signify  that  a 
kindred  piece  other  than  the  Prime  Tactical  Factor  has 
become  posted  upon  a  point  which  is  contained  within 
the  Objective  Plane. 


A  POINT  OF  LODGMENT. 
FIGURE  68. 
Black. 


White. 


STRATEGIC  PLANES. 


81 


A  Point  of  Impenetrability  is  any  point  in  the  Objec- 
tive Plane  which  in  a  given  situation  is  occupied  by  an 
adverse  piece  other  than  the  King. 


A  POINT  OF  IMPENETRABILITY. 
FIGURE  69. 

Black. 


Whitr. 


82 


MAJOR   TACTICS. 


A  Like  Point  is  any  point  in  the  Objective  Plane  of 
the  same  color  as  that  upon  which  the  adverse  King  is 
posted. 


LIKE  POINTS. 
FIGURE  70. 

Black. 





White. 


STRATEGIC  PLANES. 


83 


An  Unlike  Point  is  any  point  in  the  Objective  Plane 
of  opposite  color  to  that  upon  which  the  adverse  King 
is  posted. 


UNLIKE  POINTS. 
FIGURE  71. 

Black. 


White. 


BASIC  PROPOSITIONS  OF  MAJOR 
TACTICS. 

Following  are  the  twelve  basic  propositions  of  Major 
Tactics.  Upon  these  are  founded  all  tactical  combina- 
tions which  are  possible  in  chess  play.  The  first  four 
propositions  govern  all  calculations  whose  object  is  to 
win  adverse  pieces  ;  the  next  seven  govern  all  calcula- 
tions whose  object  is  to  queen  one  or  more  pawns ;  and 
the  final  one  governs  all  those  calculations  whose  object 
is  to  checkmate  the  adverse  King. 

A  Geometric  Symbol  is  positive  (G.  S.  P.)  when  the 
piece  to  which  it  appertains  has  the  right  of  move  in 
the  given  situation ;  otherwise  it  is  negative  (G.  S.  N.) 

In  all  situations  wherein  the  Exposed  Piece  has  the 
right  of  move  the  Point  Material  is  active  (P.  M.  A.), 
and  in  all  other  cases  the  Point  Material  is  passive 
(P.  M.  P.). 


BASIC  PROPOSITIONS. 


85 


PROPOSITION  I.  —  THEOREM. 

Given  a  Geometric  Symbol  Positive  (G.  S.  P.)  having 
one  or  more  Points  Material  (P.  M.),  then  the  kindred 
Prime  Tactical  Factor  (P.  T.  F.)  wins  an  adverse  piece. 


FIGURE  72. 

(a.) 

£luck. 


White. 
Either  to  move  and  win  a  piece. 


86 


MAJOR   TACTICS. 


FIGURE  73. 
(6.) 


Black. 


White. 
Either  to  move  and  win  a  piece. 


BASIC  PROPOSITIONS. 


87 


FIGURE  74. 
(c.) 

Black. 


While. 

Either  to  move  and  win  a  piece. 


88 


MAJOR  TACTICS. 


FIGURE  75 


Black. 


White. 
Either  to  move  and  win  a  piece. 


BASIC  PROPOSITIONS. 


89 


FIGURE  76. 


Block. 


White. 
Either  to  move  and  win  a  piece. 


90 


MAJOR   TACTICS. 


FIGURE  77. 


Black. 


White. 
Either  to  move  and  win  a  piece. 


BASIC  PROPOSITIONS. 


91 


PROPOSITION  II.  —  THEOREM. 


Given  a  Geometric  Symbol  Negative  (G.  S.  N.)  hav- 
ing two  or  more  Points  Material  Active  (P.  M.  A.),  then 
the  kindred  Prime  Tactical  Factor  (P.  T.  F.)  wins  an 
adverse  piece. 


FIGURE  78. 

(a.) 

Black. 


White. 
Black  to  move,  white  to  win  a  piece. 

NOTE  —  Black,  even  with  the  move,  can  vacate  only 
one  of  the  vertices  of  the  white  geometric  symbol. 
Therefore  the  remaining  black  piece  is  lost,  according  to 
Prop.  I. 


92 


MAJOR   TACTICS. 


FIGURE  79. 

(6.) 
Black. 


White. 
Black  to  move,  white  to  win  a  piece. 

NOTE.  —  Black,  even  with  the  move,  cannot  vacate 
the  perimeter  of  the  white  Knight's  octagon  ;  conse- 
quently the  remaining  black  piece  is  lost,  according  to 
Prop.  I. 


BASIC  PROPOSITIONS. 


93 


FIGURE  80. 


Black. 


White. 


Black  to  move,  white  to  win  a  piece. 

NOTE.  —  Black,  even  with  the  move,  cannot  vacate 
the  side  of  the  white  Bishop's  triangle ;  consequently 
the  remaining  black  piece  is  lost,  according  to  Prop.  I. 


MAJOR   TACTICS. 


FIGURE  81. 
(d.) 
Black. 


White. 

Black  to  move,  white  to  win  a  piece. 

NOTE.  —  The  Knight  cannot  in  one  move  support  the 
Bishop,  neither  can  the  Bishop  occupy  its  K  2  or  K  8  to 
support  the  Knight,  as  these  points  are  commanded  by 
the  white  Rook. 


BASIC  PROPOSITIONS. 


95 


FIGURE  82. 


Black. 


White. 
Black  to  move,  white  to  win  a  piece. 

NOTE.  —  Obviously  all  those  points  to  which  the  black 
Knight  can  move  are  commanded  by  the  white  Queen. 


MAJOR   TACTICS. 


FIGURE  83. 


Black. 


White. 
Black  to  move,  white  to  win  a  piece. 

NOTE.  —  The  Bishop  cannot  support  the  Rook,  neither 
can  the  Rook  occupy  K  B  4  in  support  of  the  Bishop,  as 
that  point  is  commanded  by  the  white  King. 


BASIC  PROPOSITIONS. 


97 


PROPOSITION  III.— THEOREM. 

Given  a  Sub-Geometric  Symbol  Positive  (S.  G.  S.  P.) 
having  two  or  more  Points  Material  Passive  (P.  M.  P.), 
then  the  kindred  Prime  Tactical  Factor  (P.  T.  F.)  wins 
an  adverse  piece. 

FIGURE  84. 
(a.) 
Black. 


White. 

White  to  move  and  win  a  piece. 


NOTE.  —  The  pawn?  having  the  move,  advances  along 
its  Front  Offensive  to  that  point  where  its  logistic  sym- 
hr.j  niul  its  frt'ometric  symbol  intersect. 


98 


MAJOR  TACTICS. 


FIGURE  85. 

w 

Black. 


White. 
White  to  move  and  win  a  piece. 


NOTE.  —  The  Point  of  Command  is  that  centre  or 
vertex  where  the  logistic  symbol  and  the  geometric 
symbol  intersect. 


BASIC  PROPOSITIONS. 


FIGURE  86. 


Black. 


White. 
White  to  move  and  win  a  piece. 


NOTE.  —  The  diagram  illustrative  of  any  position  al- 
ways should  contain  the  logistic  symbol  and  the  geo- 
metric symbol  appertaining  to  the  Prime  Tactical 
Factor. 


100 


MAJOR  TACTICS. 


FIGURE  87. 

w 

Black. 


White. 
White  to  move  and  win  a  piece. 

NOTE.  —  The  Point  of  Command  and  the  points  mate- 
rial are  all  contained  in  the  same  sides  of  the  Rook's 
quadrilateral. 


BASIC  PROPOSITIONS. 


101 


FIGURE  88. 

M 

Black. 


White. 
White  to  move  and  win  a  piece. 

NOTE.  — The  Point  of  Command  is  White's  Q  5  as  the 
logistic  radii  at  Q  R  4  do  not  intersect  the  centre  or  a 
vertex  of  the  geometric  symbol. 


102 


MAJOR  TACTICS. 


FIGURE  89. 


Slack. 


White. 
White  to  move  and  win  a  piece. 


NOTE.  —  The  white  King  cannot  move  to  Q  4  nor  to 
K  3,  on  account  of  the  resistance  of  the  black  pieces. 
But  White  wins,  as  the  latter  do  not  command  K  4. 


BASIC  PROPOSITIONS. 


103 


PROPOSITION  IV.  — THEOREM. 

Given  a  piece  which  is  both  attacked  and  supported, 
to  determine  whether  the  given  piece  is  defended. 

DEFENDED  PIECE. 

FIGURE  90. 

(a.) 

Black. 


•S/s/S/SSSSJ  'S/S'S"S'SS  */SSSS"SSSi ,*"*•"*"* 

m,w n. HI 


NOTE.  —  With  or  without  the  move  the  white  Q  B  P  is 
defended.     (See  Eule  page  109.) 


104  MAJOR  TACTICS. 


SOLUTION. 

X  =  Any   piece    employed    in   the 

given  evolution. 
Y  =  Piece  attacked. 
B+R+R+Q=  Attacking  Pieces. 
B+R+R+Q=  Supporting  Pieces. 

B+R+R+Q=B+R+R+Q=  Construction  of  the  inequality. 

4  X  =  Number  of  terms  contained  in 

left  side. 
4  X  =  Number  of  terms  contained  in 

right  side. 
(B-l-R  +  R  +  Q)  —  (B  +  R  +  R  +  Q)  =  Value  of  unlike  terms. 


Thus,  the  given  piece  is  defended,  as  the  number  of 
terms  and  the  sum  of  their  potential  complements  are 
equal. 


BASIC  PROPOSITIONS. 


105 


DEFENDED  PIECE. 

FIGURE  91. 

(b.) 

Black. 


White. 

NOTE.  —  With  or  without  the  move  the  white  Q  B  P 

is  defended. 

SOLUTION. 

X  =  Any  piece    employed  in    the  given 

evolution. 

Y  =  Piece  attacked. 
B+R+Q+R=  Attacking  Pieces. 

B  +  R  -f  R  =  Supporting  Pieces. 
B  +  R  +  Q+R>B-|-R  +  R  =  Construction  of  the  inequality. 

4  X  =  Number  of  terms  contained  in  left  side. 
3  X  =  Number  of  terms  contained  in  right 

side. 

4  x  —  3  X  =  Excess  of  left-side  terms. 
(B  +  R)  -  (B  +  R)  =  Value  of  like  terms. 

Q  -  R  =  Value  of  first  unlike  term.    ? 


106 


MAJOR   TACTICS. 


Thus  the  given  piece  is  defended,  for,  although  the 
number  of  terms  contained  in  the  left  side  of  the  in- 
equality exceeds  by  one  the  number  of  terms  contained 
in  the  right  side,  the  third  term  of  the  inequality  is  an 
unlike  term,  of  which  the  initial  contained  in  the  left 
side  is  greater  than  the  initial  contained  in  the  right 
side. 


UNDEFENDED  PIECE. 

FIGURE  92. 

(a.) 

Black. 


White. 


NOTE.  —  Without  the  move  the  white  Q  B  P  is  unde- 
fended. 


BASIC  PROPOSITIONS.  '107 


SOLUTION. 

X  =  Any    piece    employed    in    the 

given  evolution. 
Y  =  Piece  attacked. 
B+R+R+Q=  Attacking  Pieces. 
B  +  R  +  R  =  Supporting  Pieces. 

B+R+R+Q>B+R+R=  Construction  of  the  inequality. 
4  X  =  Number  of  terms  contained  in 

left  side. 
3  X  =  Number  of  terms  contained  in 

right  side. 

4  X  —  3  X  =  Excess  of  left-side  terms. 
(B  +  R  +  R)  -  (B  +  R  -|-  R)  =  Value  of  unlike  terms. 

Thus,  there  being  no  unlike  terms,  and  the  number  of 
pieces  contained  in  the  left  side  exceeding  the  number 
of  pieces  contained  in  the  right  side,  the  given  piece  is 
undefended. 


108 


MAJOR   TACTICS. 


UNDEFENDED  PIECE. 

FIGURE  93. 

(b.) 
Black. 


White. 

NOTE.  —  Without  the  move  the  white  Q  B  P  is  un- 
defended. 

SOLUTION. 

X  =  Any    piece    employed    in    the 

given  evolution. 
Y  =  Piece  attacked.  • 
B+R+Q+R=  Attacking  Pieces. 

B  +  R  =  Supporting  Pieces. 
Q-fR>B  +  R  =  Construction  of  the  inequality. 
4  X  =  Number  of  terms  contained  in 

left  side. 
2  X  =  Number  of  terms  contained  in 

right  side. 

4  X  -  2  X  =  Excess  of  left-side  terms. 
(B  +  R)  -  (B  +  R)  =  Value  of  unlike  terms. 


BASIC  PROPOSITIONS.  109 

Thus  the  given  piece  is  undefended  as  there  are  no 
unlike  terms,  and  the  number  of  terms  on  the  left  side 
exceeds  the  number  of  terms  on  the  right  side. 

RULE. 

I.  Construct  an  algebraic  inequality  having  on  the 
left  side  the  initials  of  the  attacking  pieces  arranged 
in  the  order  of  their  potential  complements  from  left  to 
right;  and  on  the  right  side  the  initials  of  the  Support- 
ing  Pieces  arranged  in  the  order  of  their  potential  com- 
plements, and  also  from  left  to  right ;  then,  — 

If  the  sum  of  any  number  of  terms  taken  in  order 
from  left  to  right  on  the  left  side  of  this  inequality  is 
not  greater  than  the  sum  of  the  same  number  of  terms 
taken  in  order  from  left  to  right  on  the  right  side,  and  if 
none  of  the  terms  contained  in  the  left  side  are  less 
than  the  like  terms  contained  in  the  right  side,  the 
given  piece  is  defended. 

II.  In  all  cases  wherein  two  or  more  of  the  Attacking 
Pieces   operate  coincident  radfi   of  offence,  or  two  or 
more  of  the  Supporting  Pieces  operate  coincident  radii 
of  defence,  those  pieces  must  be  arranged  in  the  con- 
struction of  the   inequality,   not   in  the   order   of  their 
potential  complements,  but  in  the  order  of  their  proxim- 
ity to  the  given  piece.     This  applies  only  to  the  position 
of  their  initials  with  respect  to  each  other;  the  pieces 
need  not  necessarily  lie  in  sequence;  but  in  all  cases 
the  initial  of  that  piece  of  highest  potential  complement 
should  be  placed  as  far  to  the  right  on  either  side  of  the 
equality  as  possible. 


110 


MAJOR   TACTICS. 


PROPOSITION  V.    THEOREM. 

Given  a  Square  of  Progression  (S.  P.)  whose  net 
area  is  equal  to  the  net  area  of  the  adverse  square  of 
Progression,  then,  if  the  Primary  Origins  (P.  0.)  are 
situated  neither  upon  the  same  nor  adjacent  verticals, 
and  if  the  Points  of  Junction  are  situated  not  upon 
the  same  diagonal,  the  kindred  Prime  Tactical  Factor 
(P.  T.  F.)  queens  against  an  adverse  pawn. 


FIGURE  94. 

Black. 


White. 
Either  to  move  and  queen  a  pawn. 


BASIC  PROPOSITIONS. 


Ill 


PROPOSITION  VI.    THEOREM. 

Given  a  Square  of  Progression  Positive  (S.  P.  P.) 
whose  net  area  is  greater  by  not  more  than  one  hori- 
zontal than  the  net  area  of  the  adverse  Square  of  Pro- 
gression Negative  (S.  P.  N.),  then,  if  the  Primary  Origins 
(P.  0.)  are  situated  neither  upon  the  same  nor  adjacent 
verticals,  and  the  points  of  junction  are  situated  not 
upon  the  same  diagonals,  the  kindred  Prime  Tactical 
Factor  (P.  T.  F.)  queens  against  an  adverse  pawn. 


FIGURE  95. 

Slack. 


White. 
White  to  move,  both  to  queen  a  pawn. 


112 


MAJOR   TACTICS. 


PROPOSITION  VII.    THEOREM. 

Given  a  Square  of  Progression  Positive  (S.  P.  P.) 
whose  net  area  is  less  by  one  horizontal  than  the  net 
area  of  the  adverse  Square  of  Progression  Negative 
(S.  P.  N.),  then,  if  the  Primary  Origins  (P.  0.)  are  situ- 
ated not  upon  the  same  nor  adjacent  verticals,  the  kin- 
dred Prime  Tactical  Factor  (P.  T.  F.)  will  queen  and 
will  prevent  the  adverse  pawn  from  queening. 

FIGURE  96. 

Black. 


White. 


White  to  move  and  queen  a  pawn  and  prevent  the  adverse  pawn 
from  queening. 


BASIC  PROPOSITIONS. 


113 


PROPOSITION  VIII.— THEOREM. 

Given  a  Square  of  Progression  Positive  (S.  P.  P.) 
opposed  to  a  knight's  octagon,  then,  if  the  Disturbing 
Factor  (D.  F.)  is  situated  without  the  corresponding 
Knight's  octagon,  or  within  the  corresponding  Knight's 
octagon,  but  without  the  Knight's  octagon  of  next  lower 
radius  and  on  a  square  of  opposite  color  to  the  square 
occupied  by  the  kindred  pawn,  the  Prime  Tactical  Factor 
{P.  T.  F.)  queens  against  the  adverse  Knight. 


FIGURE  97. 

(a.) 
Black. 


White. 

White  to  move  and  queen  a  pawn. 


114 


MAJOR   TACTICS. 


FIGURE  98. 

(60 
Slack. 


White. 
White  to  move  and  queen  a  pawn. 

DEMONSTRATION.  —  A  pawn  queens  without  capture 
against  an  adverse  Knight,  if,  in  general,  the  Knight 
is  situated  (1)  without  the  corresponding  Knight's  octa- 
gon, or  (2)  within  the  corresponding  Knight's  octagon, 
but  without  the  Knight's  octagon  of  next  lower  radius 
and  on  a  square  of  opposite  color  to  the  square  occupied 
by  the  pawn. 

In  diagram  No.  97,  take  the  queening  point  (o)  of 
the  pawn  as  a  centre,  and  make  a  Knight's  move  to  B, 


BASIC  PROPOSITIONS.  115 

C,  D,  and  E;  connect  these  points  by  straight  lines  and 
draw  the  vertical  lines  B  A  and  E  F ;  then  the  figure 
A  B  C  D  E  F  (or  1-1)  is  part  of  an  eight-sided  figure, 
which  may  be  called,  for  brevity's  sake,  a  Knight's 
octagon  of  single  radius. 

Similarly,  describe  the  figure  G  H  I  J  K  (or  2-2) 
whose  sides  are  parallel  to  those  of  the  figure  1-1,  but 
whose  vertices  are  two  Knight's  moves  distance  from 
the  point  o ;  this  figure  may  be  called  a  Knight's  octagon 
of  double  radius. 

Now,  if  the  pawn  has  the  first  move  it  will  be  seen, 
first,  that  a  Knight  situated  anywhere  within  the  octagon 
1-1,  provided  it  be  not  en  prise  of  the  pawn  (an  assump- 
tion common  to  all  situations),  nor  at  K  B  8  nor  Q  8  (an 
exception  peculiar  to  this  situation),  will  be  able  to  stop 
the  pawn,  either  by  preventing  it  from  queening  or  by 
capturing  it  after  it  has  queened ;  secondly,  that  a 
Knight  situated  anywhere  without  the  octagon  2-2  will 
be  unable  to  stop  the  pawn  ;  and  thirdly,  that  a  Knight 
situated  anywhere  between  the  octagon  1-1  and  2-2, 
will  be  able  to  stop  the  pawn  if  it  starts  from  a  square 
of  the  same  color  as  that  occupied  by  the  pawn  (white, 
in  this  instance),  but  unable  to  do  so  if  it  starts  from 
a  square  of  the  opposite  color  (in  this  instance,  black). 

From  diagram  No.  98,  it  is  apparent  that  four 
Knight's  diagrams  can  be  drawn  on  the  surface  of  the 
chess-board,  and  the  perimeter  of  a  fifth  may  be  con- 
sidered as  passing  through  the  lower  left-hand  corner. 
In  this  diagram  the  white  pawn  is  supposed  to  start 
from  a  point  on  the  King's  Rook's  file. 

If  the  pawn  starts  from  K  R  6,  a  black  square,  and 
having  two  moves  to  make  in  reaching  the  queening 
point,  the  Knight  must  be  situated  as  in  Fig.  No.  98, 
within  the  octagon  of  single  radius,  or  on  a  black  square 


116  MAJOR  TACTICS. 

between  the  octagon  of  single  radius  and  the  octagon  of 
double  radius. 

If  the  pawn  starts  from  K  R  5,  a  white  square,  and 
having  three  moves  to  make,  the  Knight  must  be  situated 
within  the  octagon  of  double  radius,  or  on  a  white 
square  between  the  octagon  of  double  radius  and  the 
octagon  of  triple  radius  (3-3). 

If  the  pawn  starts  from  K  R  4,  a  black  square,  and 
having  four  moves  to  make,  the  Knight  must  be  situated 
within  the  octagon  of  triple  radius,  or  in  a  black  square 
between  the  octagon  of  triple  radius  and  the  octagon  of 
quadruple  radius  (4-4). 

If  the  pawn  starts  from  K  R  3,  a  white  square,  having 
five  moves  to  make,  the  Knight  must  be  situated  within 
the  octagon  of  quadruple  radius,  or  on  a  white  square 
between  the  octagon  of  quadruple  radius  and  the 
octagon  of  quintuple  radius  (5).  In  this  last  case  it 
appears  that  the  only  square  from  whence  the  Knight 
can  stop  the  pawn  is  Black's  Q  R  8. 

If  the  pawn  starts  from  K  R  2,  it  may  advance  two 
squares  on  the  first  move,  and  precisely  the  same  con- 
ditions exist  as  if  it  started  from  K  R  3. 

Still  another  octagon  may  be  imagined  to  exist  on  the 
board,  —  namely,  the  octagon  of  null  radius,  or  simply 
the  queening  point  (o),  which  is  the  centre  of  each  of 
the  other  octagons.  This  being  understood,  it  follows 
that  if  the  pawn  starts  from  KR  7,  a  white  square,  and 
having  one  move  to  make,  the  Knight  must  be  situated 
within  the  octagon  of  null  radius  (o),  i.  e.  at  White's 
K  R  8,  or,  on  a  white  square  between  the  octagon  of 
null  radius  and  the  octagon  of  single  radius,  i.  e.  at  K 
Kt  6  or  at  K  B  7. 

From  these  data  a  general  law  may  be  deduced.  In 
order  to  abbreviate  the  enunciation  of  this  law,  it  is  well 


BASIC  PROPOSITIONS.  117 

to  lay  down  these  definitions :  By  "  the  Knight's  octagon 
corresponding  to  a  pawn,"  is  meant  that  Knight's 
octagon  whose  centre  is  the  queening  point  of  the  pawn, 
and  whose  radius  consists  of  a  number  of  Knight's 
moves  equal  to  the  number  of  moves  to  be  made  by 
the  pawn  in  reaching  its  queening  point ;  and  by  "  the 
Knight's  octagon  of  next  lower  radius,"  is  meant  that 
Knight's  octagon  whose  centre  is  the  queening  point  of 
the  pawn,  and  whose  radius  consists  of  a  number  of 
Knight's  moves  one  less  than  the  number  of  moves  to  be 
made  by  the  pawn,  in  reaching  its  queening  point.  The 
law,  then,  is  as  follows :  — 

A  Knight  can  stop  a  pawn  that  has  the  move  and  is 
advancing  to  queen,  if  the  Knight  is  situated  between 
the  Knight's  octagon  corresponding  to  the  pawn  and  the 
Knight's  octagon  of  next  lower  radius,  and  on  a  square 
of  the  same  color  as  that  occupied  by  the  pawn,  or  if 
the  Knight  is  situated  within  the  Knight's  octagon  of 
next  lower  radius  ;  provided,  that  the  Knight  be  not  en 
prise  to  the  pawn,  nor  (if  the  pawn  is  at  its  sixth  square) 
en  prise  to  the  pawn  after  the  latter's  first  move. 


118 


MAJOR  TACTICS. 


PROPOSITION  IX.— THEOREM. 

Given  a  Square  of  Progression  Positive  (S.  P.  P.) 
opposed  to  a  Bishop's  triangle,  then,  if  the  given  square 
of  progression  is  the  smallest  or  the  smallest  but  one, 
and  if  the  Point  of  Junction  is  a  square  of  opposite  color 
to  that  occupied  by  the  hostile  integer,  the  kindred  Prime 
Tactical  Factor  (P.  T.  F.)  queens  without  capture  against 
the  adverse  Bishop. 

FIGURE  99. 


Black. 


White. 
"White  to  move  and  queen  a  pawn. 


BASIC  PROPOSITIONS. 


119 


PROPOSITION  X.  —  THEOREM. 

Given  a  Square  of  Progression  Positive  (S.  P.  P.) 
opposed  to  a  Rook's  quadrilateral  or  to  a  Queen's  poly- 
gon, then,  if  the  square  of  progression  is  the  smallest 
possible,  and  if  the  hostile  integer  does  not  command 
the  Point  of  Junction,  the  kindred  Prime  Tactical  Factor 
queens  without  capture  against  the  adverse  Rook  or 
Queen. 

FIGURE  100. 
(a.) 


White. 
White  to  move  and  queen  a  pawn. 


120 


MAJOR  TACTICS. 


FIGURE  101. 
(6.) 

Slack. 


White. 
White  to  move  and  queen  a  pawn. 


BASIC  PROPOSITIONS. 


121 


PROPOSITION  XI. 

Given  a  Square  of  Progression  Positive  (S.  P.  P.)  op- 
posed to  a  King's  rectangle ;  then,  if  the  given  King  is 
not  posted  on  a  point  within  the  given  square  of  pro- 
gression, the  given  pawn  queens  without  capture  against 
the  adverse  King. 

FlGUEE    102. 
(a.) 
Black. 


White  to  move  and.queen  a  pawn. 

*"* 


122 


MAJOR  TACTICS. 


FIGURE  103. 
(6.) 

Black. 


White. 
White  to  move  and  queen  a  pawn. 


BASIC  PROPOSITIONS. 


123 


PROPOSITION  XII.  —  THEOREM. 

Given  a  Geometric  Symbol  Positive  (G.  S.  P.)  or  a 
combination  of  Geometric  Symbols  Positive  which  is 
coincident  with  the  Objective  Plane  ;  then,  if  the  Prime 
Tactical  Factor  (P.  T.  F.)  can  be  posted  at  the  Point  of 
Command,  the  adverse  King  may  be  checkmated. 


FIGURE  104. 

Black. 


WMts. 

White  to  play  and  mate  in  one  move. 


SIMPLE  TACTICAL  PLANES. 


EVOLUTION  No.  1. 

FIGURE  105. 
Pawn  vs.  Pawn. 

Black. 


White. 


When  two  opposing  pawns  are  situated  on  adjacent 
verticals  and  each  on  its  Primary  Base  Line,  that  side 
which  has  not  the  move  wins  the  adverse  pawn. 


SIMPLE   TACTICAL  PLANES. 


125 


EVOLUTION  No.  2. 
FIGURE  106. 
Pawn  vs.  Pawn. 
Black. 


White. 


A  pawn  posted  at  its  Primary  Base  Line  and  either 
with  or  without  the  move,  wins  an  adverse  pawn  situated 
at  the  intersection  of  an  adjacent  vertical  with  the  sixth 
horizontal. 


126 


MAJOR  TACTICS. 


EVOLUTION  No.  3. 

FIGURE  107. 
Pawn  vs.  Pawn. 

Black. 


4 


TFMe. 


When  the  number  of  horizontals  between  two  opposing 
pawns  situated  on  adjacent  verticals  is  even,  that  pawn 
which  has  the  move  wins  the  adverse  pawn. 


SIMPLE   TACTICAL  PLANES. 


127 


EVOLUTION  No.  4. 

FIGURE  108. 

Pawn  vs.  Pawn. 

Black. 


White 


When  the  number  of  horizontals  between  two  opposing 
pawns  situated  on  adjacent  verticals,  is  odd,  that  pawn 
which  has  not  to  move  wins  the  adverse  pawn  ;  provided 
the  position  is  not  that  of  Evolution  No.  2. 


w 


128 


MAJOR  TACTICS. 


EVOLUTION  No.  5. 

FIGURE  109. 
Pawn  vs.  Knight. 

Slack. 


White. 


Whenever  a  pawn  altitude  is  intersected  by  the  per- 
iphery of  an  adverse  Knight's  octagon,  then,  if  the  pawn 
has  not  crossed  the  point  of  intersection,  the  adverse 
Knight  wins  the  given  pawn. 


SIMPLE  TACTICAL  PLANES. 


129 


EVOLUTION  No.  6. 
FIGURE  110. 

Knight  vs.  Knight. 


White. 


A  Knight  posted  at  R 1  or  R  8,  and  having  to  move, 
is  lost  if  all  the  points  on  its  periphery  are  contained  in 
an  adverse  Knight's  octagon. 


130 


MAJOR  TACTICS. 


EVOLUTION  No.  7. 

FIGURE  111. 
Bishop  vs.  Pawn. 

Black. 


White. 


Whenever  a  pawn's  altitude  intersects  a  Bishop's 
triangle,  then,  if  the  pawn  has  not  crossed  the  point  of 
intersection,  the  adverse  Bishop  wins  the  given  pawn. 


SIMPLE   TACTICAL  PLANES. 


131 


EVOLUTION  No.  8. 

FIGURE  112. 
Bishop  vs.  Knight. 

Black. 


White. 


A  Knight  posted  at  R 1  or  R  8,  and  with  or  without 
the  move,  is  lost  if  all  the  points  on  its  periphery  are 
contained  in  the  same  side  of  the  Bishop's  triangle. 

NOTE.  —  The  B  will  equally  win  if  posted  at  Q  8. 


132 


MAJOR  TACTICS. 


EVOLUTION  No.  9. 

FIGURE  113. 

Bishop  vs.  Knight. 

Black. 


White. 


A  Knight  posted  at  R  2,  R  7,  Kt  1,  or  Kt  8,  and  having 
to  move,  is  lost,  if  all  the  points  on  its  periphery  are 
contained  in  the  sides  of  an  adverse  Bishop's  triangle. 


SIMPLE   TACTICAL  PLACES. 


133 


EVOLUTION  No.  10. 

FIGURE  114. 
Bishop  vs.  Knight. 

Black. 


White. 


A  Knight  posted  at  R  4,  R  5,  K  1,  K  8,  Q  1,  or  Q  8, 
and  having  the  move,  is  lost  if  all  the  points  on  its 
periphery  are  contained  in  the  sides  of  an  adverse 
Bishop's  triangle. 


134 


MAJOR  TACTICS. 


EVOLUTION  No.  11. 

FIGURE  115. 

Rook  vs.  Pawn. 

Black. 


White. 


Whenever  a  pawn  altitude  intersects  a  Rook's  quad- 
rilateral, then,  if  the  pawn  has  not  crossed  the  point  of 
intersection,  the  adverse  Rook  wins  the  given  pawn. 

NOTE Obviously,  whenever  a  pawn  altitude  is  coin- 
cident with  one  side  of  a  Rook's  quadrilateral,  all  the 
points  are  points  of  intersection  and  the  pawn  is  liable 
to  capture  when  crossing  each  one. 


SIMPLE   TACTICAL  PLANES. 


135 


EVOLUTION  No.  12. 

FIGURE  116. 
Rook  vs.  Knight. 

Black. 


A  Knight  posted  at  R 1  or  R  8,  and  having  to  move, 
is  lost  if  all  the  points  on  its  perimeter  are  contained  in 
the  sides  of  an  adverse  Rook's  quadrilateral. 

NOTE.  —  Obviously  the  R  would  equally  win  if  posted 
-at  Q  B  6. 


136 


MAJOR  TACTICS. 


EVOLUTION  No.  13 
FIGURE  117. 
Rook  vs.  Knight. 
Black. 


White. 


A  Knight  posted  at  R  2,  R  7,  Kt  1,  or  Kt  8,  and  having 
to  move,  is  lost  if  all  the  points  on  its  periphery  are  con- 
tained in  the  sides  of  an  adverse  Rook's  quadrilateral. 


SIMPLE   TACTICAL  PLANES. 


137 


EVOLUTION  No.  14. 

FIGURE  118. 

Rook  vs.  Knight. 

Black. 


While. 


A  Knight  posted  at  Kt  2,  or  Kt  7,  and  having  to  move, 
is  lost  if  all  the  points  on  its  perimeter  are  contained 
in  the  sides  of  an  adverse  Rook's  quadrilateral. 


138 


MAJOR  TACTICS. 


EVOLUTION  No.  15. 

FIGURE  119. 
Queen  vs.  Pawn. 

Black 


White. 

Whenever  a  pawn  altitude  intercepts  an  adverse 
Queen's  polygon,  then,  if  the  pawn  has  not  crossed  the 
point  of  intersection,  the  adverse  Queen  wins  the  given 
pawn. 

NOTE.  —  The  Q  will  equally  win  if  posted  at  Q  B 1,  Q 
R 1,  K  1,  K  B 1,  K  Kt  1,  K  R 1,  K  3,  K  B  4,  K  Kt  5,  K  R 
6,  Q  B  3,  Q  Kt  2,  Q  R  3,  Q  B  4,  Q  B  5,  Q  B  6,  Q  B  7,  or 
Q  B  8. 


SIMPLE   TACTICAL  PLANES. 


139 


EVOLUTION  No.  16. 

FIGURE  120. 
Queen  vs.  Knight. 

Black. 


White. 


A  Knight  posted  at  R 1  or  R  8,  and  having  to  move,  is 
lost  if  all  the  points  in  its  perimeter  are  contained  in 
the  sides  of  an  adverse  Queen's  polygon. 

NOTE.  —  The  Q  will  equally  win  if  posted  at  Q  R  5, 
Q  R  7,  Q  Kt  8,  Q  B  6,  Q  B  5  or  Q  8. 


140 


MAJOR   TACTICS. 


EVOLUTION  No.  17. 
FIGURE  121. 

Queen  vs.  Knight. 
Black. 


White. 


A  Knight  posted  at  R  2,  R  7,  Kt  1,  or  Kt  8,  and  having 
to  move,  is  lost  if  all  the  points  on  its  perimeter  are 
contained  in  the  sides  of  an  adverse  Queen's  polygon. 

NOTE.  —  The  Q  will  equally  win  if  posted  at  Q  7,  K  8, 
or  Q  B  5. 


SIMPLE   TACTICAL  PLANES. 


141 


EVOLUTION  No.  18. 

FIGURE  122. 

Queen  vs.  Knight. 

Black. 


White. 


A  Knight  posted  at  R  4,  R  5,  K 1,  K  8,  Q 1,  or  Q  8,  and 
having  to  move,  is  lost  if  all  the  points  on  its  perimeter 
are  contained  in  the  sides  of  an  adverse  Queen's  polygon. 

NOTE.  —  The  Q  will  equally  win  if  posted  at  Q  5. 


142 


MAJOR  TACTICS. 


EVOLUTION  No.  19. 

FIGURE  123. 

Queen  vs.  Knight. 

Black. 


White. 


A  Knight  posted  at  Kt  2  or  Kt  7,  and  having  to  move, 
is  lost  if  all  the  points  on  its  periphery  are  contained  in 
the  sides  of  an  adverse  Queen's  polygon. 


SIMPLE   TACTICAL  PLANES. 


143 


EVOLUTION  No.  20. 

FIGURE  124. 

King  vs.  Pawn. 

Black. 


White. 

Whenever  the  centre  of  a  King's  rectangle  is  con- 
tained in  the  square  of  progression  of  a  pawn;  then 
the  adverse  King  wins  the  given  pawn. 

NOTE.  —  Obviously  the  King  would  equally  win  if 
posted  on  any  square  from  the  first  to  the  third  hori- 
zontal inclusive,  the  King's  Rook's  file  excepted. 


144 


MAJOR   TACTICS. 


EVOLUTION  No.  21. 

FIGURE  125. 

King  vs.  Knight. 

Black. 


While. 


A  Knight  posted  at  El  or  E, 8,  and  having  to  move, 
is  lost  if  all  the  points  on  its  periphery  are  contained  in 
the  sides  of  an  adverse  King's  rectangle. 

NOTE.  —  The  K  would  equally  win  if  posted  at  Q  B  6. 


SIMPLE   TACTICAL  PLANES. 


145 


EVOLUTION  No.  22. 

FIGURE  126. 

Two  Pawns  vs.  Knight. 

Black. 


Whitt. 


A  Knight  situated  at  R  1,  and  having  to  move,  is  lost 
if  all  the  points  on  its  perimeter  are  contained  in  two 
adverse  pawn  triangles. 

NOTE.  —  The  pawns  will  equally  win  if  posted  at  Q  6 
and  Q  B  5  ;  or  at  Q  R  5  and  Q  Kt  6. 


MAJOR  TACTICS. 


EVOLUTION  No.  23. 

FIGURE  127. 

Two  Pawns  vs.  Bishop. 

Black. 


A  Bishop  posted  at  R 1,  and  with  or  without  the  move, 
is  lost  if  the  point  which  it  occupies  is  one  of  the  verti- 
ces of  a  pawn's  triangle. 

NOTE.  —  The  pawns  equally  win  if  posted  at  QB6 
and  Q  Kt  7. 


SIMPLE   TACTICAL  PLANES. 


147 


EVOLUTION  No.  24. 

FIGURE  128. 

Pawn  and  Knight  vs.  Knight. 
Black. 


Whenever  a  point  of  junction  is  the  vertex  of  a  mathe- 
matical figure  formed  by  the  union  of  the  logistic 
symbol  of  a  pawn  with  an  oblique,  diagonal,  horizontal, 
or  vertical  from  the  logistic  symbol  of  any  kindred 
piece  ;  then  the  given  combination  of  two  kindred  pieces 
wins  any  given  adverse  piece. 

NOTE.  —  Obviously  it  is  immaterial  what  the  kindred 
piece  may  be,  so  long  as  it  operates  a  radius  of  attack 
against  the  point  Q  8  ;  nor  what  the  adverse  piece  may 
be,  nor  what  its  position,  so  long  as  it  does  not  attack 
the  white  pawn  at  Q  7. 


148 


MAJOR   TACTICS. 


EVOLUTION  No.  25. 

FIGURE  129. 

Pawn  and  Knight  vs.  Bishop. 
Black. 


White. 

Whenever  a  piece  defending  a  hostile  point  of  junc- 
tion is  attacked,  then,  if  the  point  of  junction  and  all 
points  on  the  periphery  of  the  given  piece  wherefrom  it 
defends  the  point  of  junction,  are  contained  in  the 
geometric  symbol  which  appertains  to  the  adverse  piece, 
the  piece  defending  a  hostile  point  of  junction  is  lost. 


SIMPLE   TACTICAL  PLANES. 


149 


EVOLUTION  No.  26. 

FIGURE  130. 

Bishop  and  Pawn  vs.  Bishop. 
Black. 


White. 

Whenever  an  adjacent  Point  of  Junction  is  com- 
manded by  a  kindred  piece,  the  adverse  defending  piece 
is  lost. 

NOTE.  —  Obviously,  it  is  immaterial  what  may  be 
either  the  kindred  piece  or  the  adverse  piece ;  the  white 
pawn  queens  by  force,  and  the  kindred  piece  wins  the 
adverse  piece,  which,  of  course,  is  compelled  to  capture 
the  newly  made  Queen. 


150 


MAJOR   TACTICS. 


EVOLUTION  No.  27. 

FIGUKB  131. 

Eook  and  Pawn  vs.  Rook. 
Black. 


?  M 

*»  „  ...,y/'///"//',. 


White. 


NOTE.  —  White  wins  easily  by  R  to  K  7  supporting  the 
kindred  pawn ;  followed  by  R  to  K  8  upon  the  removal  of 
the  black  Rook  from  Q  1. 


SIMPLE  TACTICAL  PLANES. 


151 


EVOLUTION   No.  28. 

FIGURE  132. 
Two  Knights  vs.  Knight. 

Black. 


White. 


A  Knight  having  to  move  is  lost  if  all  the  points  in  its 
periphery  are  commanded  by  adverse  pieces. 


152 


MAJOR   TACTICS. 


EVOLUTION  No.   29. 

FIGURE  133. 

Knight  and  Bishop  vs.  Knight. 
Black. 


White. 


NOTE.  —  White  wins  by  Kt  to  Q  6,  or  Kt  to  K  7,  thus 
preventing  the  escape  of  the  adverse  Knight  via  Q  B  1. 


SIMPLE   TACTICAL  PLANES. 


153 


EVOLUTION  No.  30. 

FIGURE  134. 

Rook  and  Knight  vs.  Knight. 
Black. 


White 


NOTE.  —  White  wins  by  Kt  to  K  5,  thus  preventing  the 
escape  of  the  adverse  Knight  via  Q  B  3  and  Q  B  5. 


154 


MAJOR  TACTICS. 


EVOLUTION  No.  31. 

FIGURE  135. 

Queen  and  Knight  vs.  Knight. 
Black. 


White. 


NOTE.  —  White  wins  if  Black  has  to  move. 


SIMPLE   TACTICAL  PLANES. 


155 


EVOLUTION  No.  32. 

FIGURE  136. 

King  and  Knight  vs.  Knight. 
Black. 


White. 


NOTE.  —  White  wins  if  Black  has  to  move. 


156 


MAJOR  TACTICS. 


EVOLUTION  No.  33. 

FIGURE  137. 
Queen  and  Bishop  VB.  Knight. 

Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


SIMPLE   TACTICAL  PLANES 


157 


EVOLUTION  No.  34. 

FIGURE  138. 

Queen  and  Rook  rs.  Knight. 
Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


158 


MAJOR  TACTICS. 


EVOLUTION  No.  35. 

FIGURE  139. 

King  and  Queen  vs.  Knight. 
Black, 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


COMPOUND   TACTICAL  PLANES. 


EVOLUTION  No.  36. 

FIGURE  140. 
Pawn  vs.  Two  Knights. 

Black. 


VTiite. 

Whenever  two  adverse  pieces  are  posted  on  the  verti- 
ces of  a  pawn's  triangle  and  on  the  same  horizontal, 
then  if  neither  piece  commands  the  remaining  vertex, 
the  given  pawn,  having  to  move,  wins  one  of  the  adverse 
pieces. 

NOTE.  —  White  wins  by  P  to  K  4.  The  pawn  would 
equally  win  if  posted  at  K  3. 


160 


MAJOR  TACTICS. 


EVOLUTION  No.  37. 

FIGURE  141. 

Knight  vs.  Rook  and  Bishop. 
Black. 


White. 


Whenever  two  adverse  pieces  are  situated  on  the 
perimeter  of  a  Knight's  octagon,  then  if  neither  piece 
commands  the  centre  point  nor  can  support  the  other 
only  by  occupying  another  point  on  the  perimeter  of  the 
said  octagon,  the  given  Knight,  having  to  move,  wins  one 
of  the  adverse  pieces. 


COMPOUND  TACTICAL  PLANES. 


161 


EVOLUTION  No.  38. 

FIGURE  142. 

Knight  rs.  King  and  Queen. 
Black. 


WhUf. 


Whenever  the  adverse  King  is  situated  on  the  perime- 
ter of  any  opposing  geometric  symbol,  another  point  on 
which  is  occupied  by  an  unsupported  adverse  piece  which 
the  King  cannot  defend  by  a  single  move,  or  by  another 
adverse  piece  superior  in  value  to  the  attacking  piece, 
then  the  given  attacking  piece  makes  a  gain  in  adverse 
material. 

NOTE.  —  For  after  the  check  the  white  Knight  takes 
an  adverse  Queen  or  Rook,  regardless  of  the  fact  that 
itself  is  thereby  lost. 


162 


MAJOR  TACTICS. 


EVOLUTION  No.  39. 

FIGURE  143. 
Bishop  vs.  Two  Pawns. 

Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


COMPOUND   TACTICAL  PLANES. 


163 


EVOLUTION  No.  40. 

FIGURE  144. 
Bishop  vs.  King  and  Pawn. 

Black. 


White. 


NOTE.  —  White  wins  by  checking  at  Q  Kt  3,  for  the 
black  King  is  not  able  to  defend  the  pawn  in  one  move. 


164 


MAJOR  TACTICS. 


EVOLUTION  No.  41. 

FIGURE  145. 

Bishop  vs.  King  and  Knight. 
Black. 


White. 


NOTE.  —  White  wins  by  B  to  Q  Kt  3  for  Black  is  un- 
able to  defend  the  Knight  in  one  move. 


COMPOUND   TACTICAL  PLANES. 


165 


EVOLUTION  No.  42. 

FIGURE  146. 
Bishop  vs.  Two  Knights. 

Black. 


White. 


NOTE.  —  White  wins  by  B  to  Q  5  as  neither  of  the  ad- 
verse pieces  are  able  to  support  the  other  in  a  single 
move. 


166 


MAJOR   TACTICS. 


EVOLUTION  No.  43. 

FIGURE  147. 

Bishop  vs.  King  and  Knight. 
Black. 


White. 


NOTE.  —  White  wins  by  B  to  Q  B  4  (ck),  for  the  ad- 
verse King  is  unable  to  support  the  black  Knight  in  a 
single  move. 


COMPOUND  TACTICAL  PLANES. 


167 


EVOLUTION  No.  44. 

FIGURE  148. 

Rook  vs.  Two  Knights. 

Black. 


Whenever  two  Knights  are  simultaneously  attacked 
by  an  adverse  piece,  then  if  one  of  the  Knights  has  to 
move,  the  adverse  piece  wins  one  of  the  given  Knights. 


168 


MAJOR  TACTICS. 


EVOLUTION  No.  45. 

FIGURE  149. 
Rook  vs.  Knight  and  Bishop. 

Black. 


White. 


Whenever  a  Knight  and  a  Bishop  occupying  squares 
opposite  in  color,  or  of  like  color  but  unable  to  support 
each  other  in  one  move,  are  simultaneously  attacked, 
then,  either  with  or  without  the  move,  the  adverse  piece 
wins  the  given  Bishop  or  the  given  Knight. 


COMPOUND  TACTICAL  PLANES. 


169 


EVOLUTION  No.  46. 

FIGURE  150. 

Rook  vs.  Knight  and  Bishop. 
Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


170 


MAJOR  TACTICS. 


EVOLUTION  No.  47. 

FIGURE  151. 

Queen  vs.  Knight  and  Bishop. 
Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


COMPOUND   TACTICAL  PLANES. 


171 


EVOLUTION  No.  48. 

FIGURE  152. 

Queen  vs.  Knight  and  Bishop. 
Black. 


White 


NOTE.  —  White  wins  either  with  or  without  the  move. 


172 


MAJOR  TACTICS. 


EVOLUTION  No.  49. 

FIGURE  153. 
Queen  vs.  Rook  and  Knight. 

Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


COMPOUND   TACTICAL  PLANES. 


173 


EVOLUTION  No.  50. 

FIGURE  154. 
Queen  vs.  Rook  and  Bishop. 

Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


174 


MAJOR   TACTICS. 


EVOLUTION  No.  51. 
FIGURE  155. 

King  vs.  Knight  and  Pawn. 
Slack. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


COMPOUND   TACTICAL  PLANES.  175 

4% 


DEVOLUTION  No.  52. 


FIGURE  156. 


King  vs.  Bishop  and  Pawn. 
Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


c^f-s 


176 


MAJOR   TACTICS. 


EVOLUTION  No.  53. 

FIGURE  157. 

King  vs.  King  and  Pawn. 
Black. 


!JL 


White. 


NOTE.  —  White  loses  if  he  has  to  move,  and  wm&  &e  „, 
if  he  has  not  to  move. 


COMPOUND   TACTICAL  PLANES. 


Ill 


EVOLUTION  No.  54 

FIGURE  158. 
Knight  vs.  Three  Pawns. 

Black. 


White. 


NOTE.  —  White,  if  he  has  not  to  move,  will  win  all  the 
adverse  pawns. 


178 


MAJOR  TACTICS. 


EVOLUTION  No.  55. 

FIGURE  159. 
Bishop  vs.  Three  Pawns. 

Black. 


White. 


NOTE.  —  White,  if  he  has  not  to  move,  wins  all  the  ad- 
verse pawns. 


COMPOUND   TACTICAL  PLANES. 


179 


EVOLUTION  No.  56. 

FIGURE  160. 
Rook  vs.  Three  Pawns. 

Slack. 


While. 


NOTE.  —  White,  if  he  has  not  to  move,  will  win  all 
the  adverse  pawns,  ^^  W«4t>  »*<rv*    *w<  ^-  fcKf  /, 

/  ' 


130 


MAJOR  TACTICS. 


EVOLUTION  No.  57. 

FIGURE  161. 
King  vs.  Three  Pawns. 

Black. 


White. 


NOTE.  —  White,  if  he  has  not  to  move,  will  win  all 
the  adverse  pawns. 


COMPOUND   TACTICAL  PLANES. 


181 


EVOLUTION  No.  68. 

FIGURE  162. 
Knight  vs.  Bishop  and  Pawn. 

Slack. 


Wftitf. 


<*' 


. 


NOTE.  —  White,  with  the  move,  wins'  by  Kt  to  K  B  8, 
as  both  the  black  pieces  are  simultaneously  attacked 
and  will  not  mutually  support  each  other  after  Black's 
next  move. 


182 


MAJOR   TACTICS. 


EVOLUTION  No.  59. 

FIGURE  163. 

Bishop  vs.  Bishop  and  Pawn. 
Black. 


White. 


NOTE.  —  White  wins  either  with  or  without  the  move. 


COMPLEX  TACTICAL  PLANES. 


EVOLUTION  No.  60. 

FIGURE  164. 

Knight  and  Pawn  vs.  King  and  Queen. 
Black. 


White. 


NOTE.  —  By  the  sacrifice  of  the  pawn  by  P  to  Q  5  (ck) 
all  the  pieces  become  posted  on  the  perimeter  of  the 
same  Knight's  octagon,  and  White,  having  the  move, 
v.  :  n,  in  accordance  with  Prop.  IV. 


184 


MAJOR  TACTICS. 


EVOLUTION  No.  61. 

FIGURE  165. 

Knight  and  Pawn  vs.  King  and  Queen. 
Slack. 


White. 


NOTE.  —  White,  having  the  move,  wins  by  P  to  Kt  8 
(queening),  followed  by  Kt  to  K  B  6  (ck). 


COMPLEX  TACTICAL  PLANES 


185 


EVOLUTION  No.  62. 

FIGURE  166. 
Bishop  and  Pawn  vs.  King  and  Queen 

Black. 


White. 


NOTE.  —  White,  having  the  move,  wins  by  sacrificing 
the  pawn  by  P  to  Q  B  4  (ck)  and  thus  bringing  all  the 
pieces  on  the  perimeter  of  the  same  Bishop's  triangle. 


186 


MAJOR   TACTICS. 


EVOLUTION  No    63. 

FIGURE  167. 
Knight  and  Bishop  vs.  King  and  Queen. 

Slack. 


vULf 


White. 


NOTE.  —  White,  having  the  move,  wins  by  B  to  K  B  7 
(ck). 


COMPLEX  TACTICAL  PLANES. 


187 


EVOLUTION  No.  64. 

FIGURE  168. 
Bishop  and  Knight  vs.  King  and  Queen. 

Black. 


White. 


NOTE.  — White,  having  the  move,  wins  by  B  to  Q  5 
(ck),  followed  by  Kt  to  K  B  6  (ck). 


188 


MAJOR   TACTICS. 


EVOLUTION  No.  65. 

FIGURE  169. 

Knight  and  Bishop  vs.  King  and  Queen. 
Slack. 


White. 


NOTE.  —  White,  having  the  move,  wins  by  B  to  Q  5, 
followed  by  Kt  to  K  B  6  (ck). 


COMPLEX  TACTICAL  PLANES. 


189 


EVOLUTION  No.  66. 

FIGUKE  170. 

Knight  and  Bishop  vs.  King  and  Queen. 
Black. 


While. 


NOTE.  —  White,  having  the  move,  wins  by  B  to  K  Kt  7 
(ck),  followed  by  Kt  to  K  B  5  (ck). 


190 


MAJOR   TACTICS. 


EVOLUTION  No.  67. 
FIGURE  171. 

Knight  and  Bishop  vs.  King  and  Queen. 
Slack. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  B  to  Q  6  (ck), 
followed,  if  K  x  B,  by  Kt  to  K  4  (ck),  and  if  Q  x  B,  by 
Kt  to  K  B  5  (ck). 


COMPLEX  TACTICAL  PLANES. 


191 


EVOLUTION  No,  68. 
FIGURE  172. 

Knight  and  Bishop  vs.  King  and  Queen. 

Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  Kt  to  K  Kt  5 
(ck). 


192 


MAJOR  TACTICS. 


EVOLUTION  No.  69. 

FIGURE  173. 

Knight  and  Bishop  vs.  King  and  Queen. 
Black, 


White. 


NOTE.  —  White,  having  to  move,  wins  by  either  Kt  to 
K  B  2  or  Kt  to  Q  5. 


COMPLEX  TACTICAL  PLANES. 


193 


EVOLUTION  No.  70. 

FIGURE  174. 
Knight  and  Rook  vs.  King  and  Queen. 

Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  R  to  Q  Kt  5, 
followed  by  Kt  to  Q  4  (ck). 


194 


MAJOR   TACTICS. 


EVOLUTION  No.  71. 

FIGURE  175. 
Rook  and  Knight  vs.  King  and  Queen. 

Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  B,  to  Q  8  (ck), 
followed  by  Kt  to  K  6  (ck). 


COMPLEX  TACTICAL  PLANES. 


195 


EVOLUTION  No.  72. 

FIGURE  176. 

Rook  and  Knight  vs.  King  and  Queen. 
Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  R  to  K  B  5 
(ck),  followed  by  Kt  to  Q  4  (ck). 


196 


MAJOR   TACTICS. 


EVOLUTION  No.  73. 

FIGURE  177. 

Queen  and  Bishop  vs.  King  and  Queen, 
Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  B  to  K  Kt  4 
(ck). 


COMPLEX  TACTICAL  PLANES. 


197 


EVOLUTION  No.  74. 

FIGURE  178. 
Queen  and  Rook  vs.  King  and  Queen. 

Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  R  to  K  B  6 
(ck). 


198 


MAJOR  TACTICS. 


EVOLUTION  No.  75. 

FIGURE  179. 

Bishop  and  Pawn  vs.  King  and  Knight. 
Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  P  to  Q  8 
(queening),  followed  by  B  to  K  7  (ck). 


COMPLEX  TACTICAL  PLANES. 


199 


EVOLUTION  No.  76. 

FIGURE  180. 
Bishop  and  Pawn  vs.  King  and  Bishop. 

Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  B  to  K  B 
(ck),  followed  by  P  to  Q  B  8  (queening). 


200 


MAJOR  TACTICS. 


EVOLUTION  No.  77. 

FIGURE  181. 
Bishop  and  Pawn  vs.  Bishop  and  Knight. 

Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  material  by  P 
to  Q  8  (queening). 


COMPLEX  TACTICAL  PLANES. 


201 


EVOLUTION  No.  78. 

FIGURE  182. 
Bishop  and  Pawn  vs.  Rook  and  Knight. 

Black. 


While. 


NOTE.  —  White,  having  to  move,  wins  material  by  P 
to  K  8  (queening),  followed  by  B  to  Q  7. 


202 


MAJOR  TACTICS. 


EVOLUTION  No.  79. 

FIGURE  183. 

Bishop  and  Pawn  us.  King  and  Queen. 
Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  P  to  K  B  8 
(queening),  followed  by  B  to  Q  Kt  4  (ck). 


COMPLEX  TACTICAL  PLANES. 


203 


EVOLUTION  No.  80. 

FIGURE  184. 
Hook  and  Pawn  vs.  King  and  Bishop. 

Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  P  to  K  7,  fol- 
lowed, if  B  x  P,  by  R  to  K  8.  Otherwise,  the  pawn 
queens  and  wins. 


204 


MAJOR  TACTICS. 


EVOLUTION  No.  81. 

FIGUBE  185. 

Rook  and  Pawn  vs.  King  and  Rook. 
Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  P  to  K  8 
(queening),  and  followed,  if  K  X  Q,  by  R  to  R  8  (ck)  and 
RtoRT  (ck). 


COMPLEX  TACTICAL  PLANES. 


205 


EVOLUTION  No.  82. 

FIGURE  186. 

Rook  and  Pawn  r*.  King  and  Queen. 
Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  Rto  K  B  8 
(ck),  followed  by  P  to  Q  8  (queening). 


206 


MAJOR  TACTICS. 


EVOLUTION  No.  83. 
FIGURE  187. 

Queen  and  Pawn  vs.  Rook  and  Bishop. 
Black. 


t      m 


White. 


NOTE.  —  White,  having  to  move,  wins  by   P  to  Q  8 
(queening),  followed,  if  B  x  Q,  by  Q  to  Q  7. 


COMPLEX  TACTICAL  PLANES. 


207 


EVOLUTION  No.  84. 

FIGURE  188. 

Queen  and  Pawn  vs.  Rook  and  Knight. 
Black. 


White. 


NOTE.  —  White,  having  to  move,  wins   by  P  to  R  8 
(queening),  followed,  if  R  x  Q,  by  Q  to  K  Kt  7. 


208 


MAJOR  TACTICS. 


EVOLUTION  No.  85. 
FIGURE  189. 

Queen  and  Pawn  vs.  Bishop  and  Knight. 

Black. 


NOTE.  —  White,  having  to  move,  wins  by  P  to  K  6, 
followed,  if  Kt  x  P,  by  either  Q  to  K  4  or  Q  to  K  8. 


COMPLEX  TACTICAL  PLANES. 


209 


EVOLUTION  No.  86. 

FIGURE  190. 
King  and  Pawn  vs.  Bishop  and  Knight. 

Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  P  to  Q  8 
(queening),  followed,  if  B  x  Q,  by  K  x  Kt. 


210 


MAJOR   TACTICS. 


EVOLUTION  No.  87. 
FIGURE  191. 

King  and  Pawn  vs.  Two  Knights. 
Black. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  P  to  Q  8 
(queening). 


SIMPLE  LOGISTIC  PLANES. 


EVOLUTION  No.  88. 
FIGURE  192. 

Pawn  vs.  Pawn. 
Black. 


White. 


NOTE.  —  Either  to  move  and  queen  without  capture. 


212 


MAJOR   TACTICS. 


EVOLUTION  No.  89. 

FIGURE  193. 

Pawn  vs.  Pawn. 

Black. 


. 

'//////////s.     dH^ 


White. 


NOTE.  —  White,  having  to  move,  wins,  first  queening 
his  pawn  and  then  with  the  newly  made  queen  captur- 
ing the  adverse  pawn.  If  white  has  not  the  move,  the 
black  pawn  queens  without  capture. 


SIMPLE  LOGISTIC  PLANES. 


213 


EVOLUTION  No.  90. 

FIGURE  194. 
Pawn  vs.  Pawn. 
Black. 


White. 


XOTE.  —  White,  either   with   or  without  the   move, 
queens  and  captures  the  adverse  pawn. 


214 


MAJOR   TACTICS. 


EVOLUTION  No.  91. 

Fioure  195. 
Pawn  vs.  Knight. 
Black. 


White. 


NOTE.  —  White,  having    to    move,   queens    without 
capture. 


SIMPLE  LOGISTIC  PLANES. 


215 


EVOLUTION  No.  92. 

FIGURE  196. 
Pawn  vs.  Bishop. 

Black. 


White. 


NOTE.  —  White,  either  with   or    without  the    move, 
queens  without  capture. 


MAJOR  TACTICS. 


EVOLUTION  No.  93. 

FIGURE  197. 

Pawn  vs.  King. 

Black. 


White. 


NOTE.  —  White,    having    to    move,  queens    without 
capture. 


SIMPLE  LOGISTIC  PLANES. 


217 


EVOLUTION  No.  94. 

FIGURE  198. 
Pawn  and  Knight  vs.  Queen  or  Rook. 

Black. 


White. 

Whenever  a  Queen  or  Rook  defending  a  hostile  Point 
of  Junction  has  not  the  move,  then  if  an  adverse  piece 
can  be  in  one  move  posted  on  the  adjacent  vertex  of  the 
pawn's  triangle,  the  given  pawn  queens  without  capture. 

XOTE.  —  It  is,  of  course,  immaterial  what  the  kin- 
dred piece  may  be,  so  long  as  it  can  occupy  the  point 
K  8  ;  or  what  the  position  of  the  defending  piece,  if  it 
does  not  attack  the  pawn  at  Q  7. 


218 


MAJOR   TACTICS. 


EVOLUTION  No.  95. 

FIGURE  199. 
Bishop  and  Pawn  vs.  King  and  Rook. 

Slack. 


White. 


NOTE.  —  White,  having  to  move,  wins  by  B  to  K  R  3 
(ck),  followed  by  B  to  Q  B  8. 


SIMPLE  LOGISTIC  PLANES. 


219 


EVOLUTION  No.  96. 

FIGURE  200. 
Rook  and  Pawn  vs.  Rook. 

White. 


White. 


NOTE.  —  White  wins,  either  with  or  without  the  more. 


220 


MAJOR   TACTICS. 


EVOLUTION  No.  97. 

FIGURE  201. 

Knight  and  Pawn  vs.  King. 
Black. 


White. 


NOTE.  —  White,  either  with  or  without,  wins,  as 
the  black  King  cannot  gain  command  of  the  Point 
of  Junction. 


SIMPLE  LOGISTIC  PLANES. 


221 


EVOLUTION  No.  98. 

FIGURE  202. 

Rook  and  Pawn  vs.  King. 
Black. 


W/. 


White. 


NOTE.  —  White  wins,  either  with  or  without  the  move, 
as  the  adverse  King  cannot  attack  any  point  on  the  kin- 
dred pawn's  altitude. 


222 


MAJOR   TACTICS. 


EVOLUTION  No.  99. 

FIGURE  203. 
Bishop  and  Pawn  vs.  King  and  Queen. 

Black. 


White. 


NOTE.  —  White,  having  the  move,  wins  by  P  to  Q  8, 
queening  and  disclosing  check  from  the  kindred  Bishop. 


COMPOUND  LOGISTIC  PLANES. 


EVOLUTION  No.  100. 

FIGURE  204. 

Two  Pawns  vs.  Pawn. 

Black. 


Hi 


White. 


NOTE.  —  White  wins,  either  with  or  without  the  move, 
by  eliminating  the  adverse  Point  of  Resistance  by 
P  to  Q  6,  or  by  P  to  Q  Kt  6  ;  clearing  the  vertical  of 
one  or  the  other  of  the  kindred  pawns. 


224 


MAJOR  TACTICS. 


EVOLUTION  No.  101. 

FIGURE  205. 
Two  Pawns  vs.  Pawn. 

Black. 


White. 


NOTE.  —  White  wins,  either  with  or  without  the  move. 


COMPOUND  LOGISTIC  PLANES. 


EVOLUTION  No.  102. 

FIGURE  206. 
Two  Pawns  vs.  Knight. 

Black. 


White. 


NOTE.  —  White,  having  the  move,  will  queen  one  of 
the  pawns  without  capture  by  the  adverse  Knight. 


226 


MAJOR  TACTICS. 


EVOLUTION  No.  103. 

FIGURE  207. 
Two  Pawns  vs.  Knight. 

Black. 


White. 


NOTE.  —  White,  either  with  or  without  the  move,  will 
queen  one  of  the  pawns  without  capture  by  the  adverse 
Knight. 


COMPOUND  LOGISTIC  PLANES. 


227 


EVOLUTION  No.  104. 

FIGURE  208. 
Two  Pawns  vs.  Bishop. 


White. 


NOTE.  —  White,  either  with  or  without  the  move,  will 
queen  one  of  the  pawns  without  capture  by  the  adverse 
Bishop. 


228 


MAJOR   TACTICS. 


EVOLUTION  No.  105. 
FIGURE  209. 

Two  Pawns  vs.  Bishop. 
Slack. 


White. 


NOTE.  —  White,  either  with  or  without  the  move,  will 
queen  one  of  the  pawns  without  capture  by  the  adverse 
Bishop. 


COMPOUND  LOGISTIC  PLANES. 


229 


EVOLUTION  No.  106. 

FIGURE  210. 
Two  Pawns  vs.  Rook 

Black. 


White. 


NOTE.  —  White,  either  with  or  without  the  move,  will 
queen  one  of  the  pawns  without  capture  by  the  adverse 
Rook. 


230 


MAJOR  TACTICS. 


EVOLUTION  No.  107. 

FIGURE  211. 
Two  Pawns  vs.  King. 

Black. 


White. 


NOTE.  —  White,  either  with  or  without  the  move,  will 
queen  one  of  the  pawns  without  capture  by  the  adverse 
King. 


COMPOUND  LOGISTIC  PLANES. 


231 


EVOLUTION  No.  108. 

FIGURE  212. 

Two  Pawns  vs.  King. 

Black. 


While. 


NOTE.  —  White,  either  with  or  without  the  move,  will 
queen  one  of  the  pawns  without  capture  by  the  adverse 
King. 


COMPLEX  LOGISTIC  PLANES. 


EVOLUTION  No.  109. 

FIGURE  213. 

Three  Pawns  vs.  Three  Pawns. 
Black. 


White. 


NOTE.  —  White,  having  to  move,  will  queen  a  pawn 
without  capture  by  T'to  Q  6^  followed,  if  K  P  x  P,  by  P  to 
Q  B  6  ;  and  if  B  P  x  P,  by  Pto  K  6. 


COMPLEX  LOGISTIC  PLANES. 


233 


EVOLUTION  No.  110. 

FIGURE  214. 

Three  Pawns  vs.  King. 
Black. 


White 


NOTE.  —  If  White  moves,  Black  wins  all  the  pawns 
by  moving  the  King  in  front  of  that  pawn  which  ad- 
vances ;  but  if  Black  has  to  move,  one  of  the  pawns 
will  queen  without  capture  against  the  adverse  King. 

The  key  of  the  position  is  the  posting  of  the  King  in 
front  of  the  middle  pawn,  with  one  point  intervening, 
when  all  are  in  a  line  and  when  it  is  the  turn  of  the 
pawns  to  move.  Then  the  King  must  play  to  the  point 


in   frnr.1.  nf 


Tinxvn  <l-nt 


234 


MAJOR  TACTICS. 


EVOLUTION  No.  111. 

FIGURE  215. 
Three  Pawns  vs.  Queen. 

Black. 


White. 


NOTE  —  Black  wins,  either  with  or  without  the  move. 
The  key  of  this  position  is  that  the  black  Queen  wins 
if  she  is  posted  on  any  square  opposite  in  color  to  those 
occupied  by  the  pawns,  from  whence  she  commands 
the  adjacent  Point  of  Junction. 


COMPLEX  LOGISTIC  PLANES. 


235 


EVOLUTION  No.  112. 

FIGURE  216. 

Three  Pawns  vs.  King  and  Pawn. 
Black. 


White. 


NOTE.  —  White  wins,  either  with  or  without  the  move. 


SIMPLE   STRATEGIC   PLANES. 


EVOLUTION  No.  113. 

FIGURE  217. 
Knight  vs.  Objective  Plane  of  Single  Radius. 

Black. 


White. 


NOTE.  —  The  Front  Offensive  always  is  an  oblique,  and 
the  Point  of  Command  of  unlike  color  to  the  Point 
Material,  and  the  radius  a  point  on  the  perimeter  of  the 
adverse  Knight's  octagon. 


SIMPLE  STRATEGIC  PLANES. 


237 


EVOLUTION  No.  114. 

FIGURE  218. 

Knight  vs.  Objective  Plane  of  Two  Radius. 
Black. 


NOTE.  —  The  Front  Offensive  always  is  an  oblique ; 
the  Point  of  Command  of  unlike  color  to  the  Point 
Material,  and  the  radius  is  a  section  of  two  points  on 
the  adverse  Knight's  octagon. 


238 


MAJOR  TACTICS. 


EVOLUTION  No.  115. 

FIGURE  219. 
Bishop  vs.  Objective  Plane  of  Two  Radius. 

Black. 


White. 


NOTE.  —  The  Front  Offensive  always  is  a  diagonal; 
the  Point  of  Command  and  the  radius  are  of  like  color 
to  the  Point  Material,  and  the  latter  is  situated  on  the 
same  side  of  the  Bishop's  triangle  as  the  Point  of 
Command. 


SIMPLE  STRATEGIC  PLANES, 


239 


EVOLUTION  No.  116. 
FIGURE  220. 

Bishop  vs.  Objective  Plane  of  Three  Radius. 


White 


XOTE.  —  The  Front  Offensive  always  is  a  diagonal ; 
the  Point  of  Command  and  the  radius  are  of  like  color 
to  the  Point  Material,  and  the  latter  is  situated  on 
the  same  side  of  the  Bishop's  triangle  as  the  Point  of 
Command. 


240 


MAJOR  TACTICS. 


EVOLUTION  No.  117. 

FIGURE  221. 

Rook  vs.  Objective  Plane  of  Two  Radius. 
Slack. 


White. 


NOTE.  —  The  Front  Offensive  is  a  vertical  or  hori- 
zontal; the  radius  is  composed  of  one  like  and  one 
unlike  point,  and  situated  on  one  side  of  the  adverse 
Rook's  quadrilateral.  The  Point  of  Command  may  be 
either  a  like  or  an  unlike  point. 


SIMPLE  STRATEGIC  PLANES. 


241 


EVOLUTION  No.  118. 

FIGURE  222. 
Rook  vs.  Objective  Plane  of  Three  Radius. 

Black. 


White. 


NOTE.  —  The  Front  Offensive  is  a  vertical  or  hori- 
zontal ;  the  radius  is  composed  of  one  like  and  two 
unlike  points  and  situated  on  one  side  of  the  adverse 
Rook's  quadrilateral.  The  Point  of  Command  may  be 
either  a  like  or  an  unlike  point. 


242 


MAJOR  TACTICS. 


EVOLUTION  No.  119. 

FIGURE  223. 
Queen  vs.  Objective  Plane  of  Two  Kadius. 

Black. 


White. 


NOTE.  —  The  Front  Offensive  is  a  diagonal ;  the  radius 
is  composed  of  two  like  points  situated  on  the  same  side 
of  the  adverse  Queen's  polygon.  The  Point  of  Com- 
mand and  the  Point  Material  are  like  points. 


SIMPLE  STRATEGIC  PLANES. 


243 


EVOLUTION  No.   120. 

FIGDBE  224. 
Queen  vs.  Objective  Plane  of  Two  Radius. 

Black. 


White. 


NOTE.  — The  Front  Offensive  is  a  vertical  or  a  hori- 
zontal ;  the  radius  is  composed  of  one  like  and  one  un- 
like point,  contained  in  the  same  side  of  the  adverse 
Queen's  polygon.  The  Point  of  Command  may  be  either 
a  like  or  an  unlike  point. 


MAJOR  TACTICS. 


EVOLUTION  No.  121. 

FIGURE  225. 

Queen  us.  Objective  Plane  of  Three  Radius. 
Black. 


White. 


NOTE.  —  The  Front  Offensive  is  a  diagonal ;  the  radius 
is  composed  of  like  points,  contained  in  the  same  side 
of  the  adverse  Queen's  polygon.  The  Point  of  Com- 
mand and  the  Point  Material  are  like  points. 


SIMPLE  STRATEGIC  PLANES. 


245 


EVOLUTION  No.  122. 

FIGURE  226. 

Queen  vs.  Objective  Plane  of  Three  Radius. 
Black. 


iHi 


White. 


NOTE.  —  The  Front  Offensive  is  a  vertical  or  hori- 
zontal ;  the  radius  is  composed  of  one  like  and  two  un- 
like points,  contained  in  the  same  side  of  the  adverse 
Queen's  polygon.  The  Point  of  Command  may  be 
either  a  like  or  an  unlike  point. 


246 


MAJOR   TACTICS. 


EVOLUTION  No.  123. 

*    FIGURE  227. 

Queen  vs.  Objective  Plane  of  Four  Radius. 
Black. 


White. 


NOTE.  — The  Front  Offensive  is  a  vertical  or  hori- 
zontal combined  with  a  diagonal ;  the  radius  is  com- 
posed of " two  like  and  two  unlike  points,  and  these  are 
coincident  with  given  sides  of  the  Queen's  polygon. 
The  Point  of  Command  and  the  Point  Material  are  like 
points. 


COMPOUND  STRATEGIC  PLANES. 


EVOLUTION  No.  124. 

FIGURE  228. 
Pawn  and  Supporting  Factor  vs.  Objective  Plane  of  Two  Radius. 

Black. 


* 

* 


White. 

NOTE.  —  A  single  Pawn  cannot  command  any  Ob- 
jective Plane.  In  this  situation,  the  Front  Offensive  is 
a  diagonal  ;  the  radius  is  composed  of  two  like  points 
and  contained  on  the  same  side  of  the  adverse  Pawn's 
triangle.  The  Point  of  Command  and  the  Point  Mate- 
rial are  like  Points. 


248 


MAJOR  TACTICS. 


EVOLUTION  No.    125. 

FIGURE  229. 
Bishop  and  Supporting  Factor  vs.  Objective  Plane  of  Three  Radius 

Black. 


NOTE.  —  The  Front  Offensive  is  a  diagonal ;  the  radius 
is  composed  of  two  like  points,  contained  in  the  same 
side  of  the  adverse  Bishop's  triangle,  and  one  unlike 
point  contained  in  the  perimeter  of  the  supporting 
Factor.  The  Point  of  Command  is  a  like  point. 


COMPOUND  STRATEGIC  PLANES. 


249 


EVOLUTION  No.  126. 

FIGURE  230. 

Bishop  and  Supporting  Factor  vs.  Objective  Plane  of  Three  Radius. 

Block. 


While. 


NOTE.  —  The  Front  Offensive  is  made  up  of  a  diago- 
nal and  an  oblique  ;  the  radius  is  composed  of  three 
like  points,  all  of  which  are  contained  in  the  adverse 
diagonal.  The  Point  of  Command  is  a  like  point. 


250 


MAJOR   TACTICS. 


EVOLUTION  No.  127. 

FIGURE  231. 

Rook  and  Supporting  Factor  vs.  Objective  Plane  of  Three  Radius. 

Slack. 


While. 

NOTE.  — The  Front  Offensive  is  made  up  of  a  vertical 
or  horizontal  and  an  oblique ;  the  radius  is  composed  of 
two  like  and  one  unlike  point,  two  of  which  are  contained 
in  one  side  of  the  adverse  Rook's  quadrilateral  and  the 
other  in  the  perimeter  of  the  adverse  Knight's  octagon. 
The  Point  of  Command  may  be  either  a  like  or  an 
unlike  point,  and  situated  upon  either  the  horizontal 
or  vertical. 


COMPOUND  STRATEGIC  PLANES 


251 


EVOLUTION  No.  128. 

FIGURE  232. 
Rook  and  Supporting  Factor  vs.  Objective  Plane  of  Four  Radius. 

Black. 


White. 

NOTE.  —  The  Front  Offensive  consists  of  a  vertical  or 
horizontal  and  an  oblique ;  the  radius  is  composed  of  two 
like  and  two  unlike  points,  two  of  which,  both  unlike, 
are  situated  on  the  perimeter  of  an  adverse  Knight's 
octagon,  and  one  like  and  one  unlike  are  situated  on 
one  side  of  the  adverse  Rook's  quadrilateral.  The  Point 
of  Command  is  an  unlike  point,  and  is  that  point  in  the 
Objective  Plane  at  which  the  given  octagon  and  quadri- 
lateral intersect. 


252 


MAJOR   TACTICS. 


EVOLUTION  No.  129i 

FIGUKE  233. 
Rook  and  Supporting  Factor  vs.  Objective  Plane  of  Five  Radius. 

Slack. 


White. 

NOTE. — The  Offensive  Front  consists  of  a  vertical,  a 
horizontal,  and  an  oblique.  The  radius  is  composed  of 
two  like  and  of  three  unlike  points,  two  like  and  one 
unlike  points  being  contained  in  the  horizontal,  one 
like  and  two  unlike  points  being  contained  in  the  hori- 
zontal, and  one  unlike  point  in  the  oblique.  The  Point 
of  Command  is  an  unlike  point,  and  is  that  point  at 
which  the  adverse  quadrilateral  and  octagon  intersect. 


COMPOUND  STRATEGIC  PLANES. 


253 


EVOLUTION  No.  130. 

FIGURE  234. 

Queen  and  Supporting  Factor  vs.  Objective  Plane  of  Seven  Radius. 

Black. 


White. 


NOTE.  —  The  Front  Offensive  consists  of  a  horizontal, 
a  vertical,  two  diagonals,  and  two  obliques.  The  radius 
is  composed  of  three  like  and  four  unlike  points ;  three 
unlike  points  are  contained  in  the  diagonals,  two  unlike 
and  one  like  points  in  the  vertical,  one  unlike  and  two 
like  points  in  the  horizontal,  and  two  unlike  points  in 
the  obliques.  The  Point  of  Command  is  an  unlike  point, 
and  is  that  point  at  which  the  adverse  polygon  and 
octagon  intersect. 


254 


MAJOR   TACTICS. 


EVOLUTION  No.  131. 

FIGURE  235. 
Queen  and  Supporting  Factor  vs.  Objective  Plane  of  Seven  Radius 

Black. 


White. 

NOTE.  —  The  Front  Offensive  consists  of  a  vertical,  a 
horizontal,  a  diagonal,  and  an  oblique.  The  radius  is 
composed  of  five  like  points  and  two  unlike  points,  one 
like  and  two  unlike  points,  and  contained  in  both  the 
vertical  and  the  horizontal,  three  like  points  in  the 
diagonal,  and  one  in  the  oblique.  The  Point  of  Com- 
mand is  a  like  point,  and  is  that  point  at  which  the 
adverse  polygon  and  octagon  intersect. 


COMPLEX  STRATEGIC  PLANES. 


255 


COMPLEX  STRATEGIC   PLANES. 


EVOLUTION  No.  132. 
FIGURE  236. 

A  Pawn  Lodgment  in  an  Objective  Plane  of  Eight  Radius. 
Black. 


White. 


NOTE.  —  The  Queen  never  occupies  a  Point  of  Lodg- 
ment, and  consequently  she  can  only  enter  the  Objec- 
tive Plane  as  a  Prime  Tactical  Factor. 


256 


MAJOR  TACTICS. 


EVOLUTION  No.  183. 
FIGURE  237. 

A  Knight  Lodgment  in  an  Objective  Plane  of  Eight  Radius. 
Black. 


White. 


NOTE.  —  In  evolutions  combining  a  Knight  lodg- 
ment, the  Supporting  Factor  always  must  be  defended 
by  an  Auxiliary  Factor. 


COMPLEX  STRATEGIC  PLANES 


257 


EVOLUTION  No.  134. 
FIGURE  238. 

A  Bishop  Lodgment  in  an  Objective  Plane  of  Eight  Radius. 
Black. 


White. 


NOTE.  —  The  Point  of  Lodgment  must  always  be  sup- 
ported whenever  it  is  established  in  any  Objective  Plane. 


258 


MAJOR  TACTICS. 


EVOLUTION  No.  135. 

FIGURE  239. 

A  Rook  Lodgment  in  an  Objective  Plane  of  Eight  Radius. 
Black. 


White. 


NOTE.  —  This  is  the  only  manner  by  which  the  0.  P.  8 
can  be  commanded  by  two  pieces. 


COMPLEX  STRATEGIC  PLANES 


259 


EVOLUTION  No.  136. 

FIGURE  240. 

A  Pawn  Lodgment  in  Objective  Plane  of  Nine  Radius. 
Black. 


White. 


NOTE.  —  The  union  of  the  kindred  King  with  a  pawn 
lodgment  is  the  most  effective  combination  against  an 
Objective  Plane  of  nine  radii  which  does  not  contain 
the  Queen. 


260 


MAJOR   TACTICS. 


EVOLUTION  No.  137. 
FIGURE  241. 

A  Knight  Lodgment  in  an  Objective  Plane  of  Nine  Radius. 
Black. 


White. 


NOTE.  —  The  above  position  is  suggestive  of  a  very 
pretty  allegory. 


COMPLEX  STRATEGIC  PLANES. 


261 


EVOLUTION  No.  138. 

FIGURE  242. 
A  Bishop  Lodgment  in  an  Objective  Plane  of  Nine  Radius. 

Black. 


White. 


NOTE  —  This  is  the  only  manner  in  which  this  com- 
bination of  force  can  command  the  Objective  Plane  of 
nine  radii. 


262 


MAJOR  TACTICS. 


EVOLUTION  No.  139. 
FIGURE  243. 

A  Rook  Lodgment  in  an  Objective  Plane  of  Nine  Radius. 
Black. 


NOTE.  —  In  an  evolution  against  the  0.  P.  9,  and 
whenever  the  kindred  Queen  is  not  present,  three  pieces 
are  necessary  to  effect  checkmate. 


COMPLEX  STRATEGIC  PLANES. 


263 


EVOLUTION  No.  140. 
FIGURE  244. 

Command  of  an  Objective  Plane  of  Nine  Radius  by  minor  Diagonals 
and  Obliques. 

Black. 


White. 

NOTE.  —  The  student  should  observe  that  the  power 
of  the  white  force  is  derived  from  the  presence  of  the 
pawn's  diagonals.  The  white  King  is  passive  and  un- 
available for  offence  against  the  black  King,  and  with 
both  Knights  but  without  the  pawns  the  Objective  Plane 
cannot  be  commanded. 


264 


MAJOR  TACTICS. 


EVOLUTION  No.  141. 

FIGURE  245. 
Command  of  an  Objective  Plane  of  Nine  Radius  by  Diagonals. 

Black. 


White. 


NOTE.  —  In  any  combination  of  the  diagonal  pieces 
against  the  0.  P.  9,  the  Queen  is  always  the  Prime 
Tactical  Factor. 


COMPLEX  STRATEGIC  PLANES. 


265 


EVOLUTION  No.  142. 
FIGURE  246. 

Command  of  an  Objective  Plane  of  Nine  Radius  by  Verticals  and 
Horizontals. 

Black. 


White. 


NOTE.  —  The  0.  P.  9  never  can  be  commanded  by  less 
than  three  pieces. 


LOGISTICS   OF  GEOMETRIC  PLANES. 

In  each  of  the  foregoing  evolutions,  there  is  depicted 
one  of  the  basic  ideas  of  Tactics  ;  the  motif  of  which  is 
either  the  capture  of  an  opposing  piece,  the  queening  of 
a  kindred  pawn,  or  the  checkmate  of  the  hostile  King. 

The  material  manifestation  of  each  idea  is  given  by 
formations  of  opposing  forces,  upon  specified  points ; 
and  the  execution  of  the  plan  —  i.  e.  the  practical  ap- 
plication of  this  basic  idea  in  the  art  of  chess-play  —  is 
illustrated  by  the  movements  of  the  given  forces,  from 
the  given  points  to  other  given  points,  in  given  times. 

Upon  these  movements,  or  evolutions,  are  based  all 
those  combinations  in  chess-play  wherein  a  given  piece 
co-operates  with  one  or  more  kindred  pieces,  for  the 
purpose  of  reducing  the  adverse  material,  or  of  aug- 
menting its  own  force,  or  of  gaining  command  of  the 
Objective  Plane ;  and  there  is  no  combination  of  forces 
for  the  producing  of  either  or  all  of  these  results  pos- 
sible on  the  chess-board,  in  which  one  or  more  of  these 
basic  ideas  is  not  contained. 

Furthermore,  the  opposing  forces,  the  points  at  which 
each  is  posted,  and  the  result  of  the  given  evolution 
being  determinate,  it  follows  that  the  movements  of 
the  given  forces  equally  are  determinate,  and  that  the 
points  to  which  the  forces  move  and  the  verticals,  hori- 
zontals, diagonals,  and  obliques  over  which  they  move, 
may  be  specified  and  described. 

As  the  reader  has  seen,  the  movements  of  the  pieces 
in  every  evolution  take  the  form  of  straight  lines,  ex- 


LOGISTICS  OF   GEOMETRIC  PLANES.  267 

tending  from  originally  specified  points  to  other  neces- 
sary points ;  which  latter  constitute  the  vertices  of 
properly  described  octagons,  quadrilaterals,  rectangles, 
and  triangles. 

The  validity  of  an  evolution,  i.  e.  its  adaptability  to 
a  given  situation,  once  established,  the  execution  is 
purely  mechanical,  and  its  practical  application  in  chess- 
play  is  simple  and  easy ;  but  to  determine  the  validity 
of  an  evolution  in  any  given  situation  is  the  test  of 
one's  understanding  of  the  true  theory  of  the  game. 

The  secret  of  Major  Tactics  is  to  attack  an  adverse 
piece  at  a  time  when  it  cannot  move,  at  a  point  where 
it  is  defenceless,  and  with  a  force  that  is  irresistible. 

The  first  axiom  of  Major  Tactics  is  :  — 

A  piece  exerts  no  force  for  the  defence  of  the  point 
upon  which  it  stands. 

Consequently,  so  far  as  the  occupying  piece  is  con- 
cerned, the  point  upon  which  a  piece  is  posted  is  abj 
solutely  defenceless. 

The  second  axiom  of  Major  Tactics  is :  — 

A  piece  exerts  no  force  for  the  defence  of  any  verti- 
cal, horizontal,  diagonal,  or  oblique,  along  which  it  does 
not  operate  a  radius  of  offence. 

Hence  it  is  obvious  that  a  pawn  defends  only  a  minor 
diagonal ;  that  it  does  not  defend  a  vertical,  a  horizon- 
tal, a  major  diagonal,  nor  an  oblique ;  that  a  Knight 
defends  an  oblique,  but  not  a  vertical,  a  horizontal,  nor 
a  diagonal ;  that  a  Rook  defends  a  vertical  and  a  hori- 
zontal, but  not  a  diagonal  nor  an  oblique  ;  that  a  Queen 
defends  a  vertical,  a  horizontal,  and  a  diagonal,  but  not 
an  oblique,  and  that  a  King  defends  only  a  minor  verti- 
cal, a  minor  horizontal,  and  a  minor  diagonal,  and  does 
not  defend  a  major  vertical,  a  major  horizontal,  a  major 
diagonal,  nor  an  oblique. 


268  MAJOR   TACTICS. 

It  also  is  evident  that  an  attacking  movement  for  the 
purpose  of  capturing  a  hostile  piece  always  should  take 
the  direction  of  the  point  upon  which  the  hostile  piece 
stands  ;  and  that  the  attacking  force  should  be  directed 
along  that  vertical,  horizontal,  diagonal,  or  oblique, 
which  is  not  defended  by  the  piece  it  is  proposed  to 
capture. 

That  is  to  say :  the  simple  interpretation  of  Major 
Tactics  is  that  you  creep  up  behind  a  man's  back  while 
he  is  not  looking,  and  before  he  can  move,  and  while  he 
is  utterly  defenceless  you  off  with  his  head. 

This,  of  course,  is  the  crude  process.  But  it  does  not 
appertain  to  savages  alone ;  in  fact,  it  is  the  process 
usually  followed  by  so-called  educated  and  civilized  folk, 
whether  chess-players  or  soldiers ;  furthermore,  the 
final  situation  of  the  uplifted  sword  and  the  unsuspect- 
ing and  defenceless  victim  is  the  invariable  climax  of 
every  evolution  of  Major  Tactics,  whether  the  latter  be- 
longs to  war  or  to  chess. 

It  is  admitted  that  men,  whether  soldiers  or  chess- 
players, have  eyes  in  their  heads,  and  that  it  is  not 
supposable  that  they  would  permit  an  enemy  thus  to 
take  them  unawares  and  by  such  a  simple  and  un- 
sophisticated process.  Nevertheless  there  is  another 
process  which  leads  to  the  same  result;  and  this  pro- 
cess is  the  quintessence  of  science,  whether  of  war  or 
of  chess. 

These  two  methods,  one  the  crudest  and  one  the  most 
scientific  possible,  unite  at  the  point  at  which  the  sword 
is  lifted  to  the  full  height  over  the  head  of  the  unsus- 
pecting and  defenceless  enemy.  From  thence  they  act 
as  unity,  for  it  needs  no  talent  to  cut  off  a  man's  head 
who  is  incapable  of  resistance,  to  massacre  an  army 
that  is  hopelessly  routed,  nor  to  checkmate  the  adverse 


LOGISTICS  OF  GEOMETRIC  PLANES.  269 

King  in  one  move.  In  such  a  circumstance  a  butcher 
is  equal  to  Arbuthnot ;  a  Zulu  chief  to  Napoleon ;  and 
the  merest  tyro  at  chess  to  Paul  Morphy. 

To  attack  and  capture  an  enemy  who  can  neither  fight 
nor  run  is  very  elementary  and  not  particularly  edify- 
ing strategetics ;  but  to  attack  simultaneously  two  hos- 
tile bodies,  at  a  time  and  at  points  whereat  they  cannot 
be  simultaneously  defended,  is  the  acme  of  chess  and  of 
war.  In  either  case  the  result  is  identical,  and  success 
is  attained  by  the  same  means.  But  the  second  process, 
as  compared  with  the  first  process,  is  transcendental; 
for  it  consists  in  surprising  and  out-manoeuvring  two 
adversaries  who  have  their  eyes  wide  open. 

The  means  by  which  success  is  attained  in  Major 
Tactics  is  the  proper  use  of  time. 

"  He  who  gains  time  gains  everything ! "  is  the  dictum 
of  Frederic  the  Great, — a  man  who,  as  a  major  tac- 
tician, has  no  equal  in  history. 

To  illustrate  the  truth  of  this  maxim,  the  attention  of 
the  student  is  called  to  the  simple  fact  that  if,  at  the 
beginning  of  a  game  of  chess,  White  had  the  privilege  of 
making  four  moves  in  succession  and  before  Black 
touched  a  piece,  the  first  player  would  checkmate  the 
adverse  King  by  making  one  move  each  with  the  K  P 
and  the  K  B  and  two  moves  with  the  Q. 

Again,  in  any  subsequent  situation,  if  either  player 
had  the  privilege  of  making  two  moves  in  succession,  it 
is  evident  that  he  would  have  no  difficulty  in  winning 
the  game.  To  gain  this  one  move,  —  with  all  due  de- 
ference to  the  shade  of  Philidor,  —  and  not  the  play  of 
the  pawns,  is  the  soul  of  chess. 

But  it  is  easy  to  see  that  gain  of  time  can  be  of  little 
advantage  to  a  man  who  does  not  understand  the  proper 
use  of  time ;  and  it  is  equally  easy  to  see,  if  time  is 


270  MAJOR   TACTICS. 

to  be  properly  utilized  in  an  evolution  of  Major  Tactics, 
that  a  thorough  knowledge  of  the  forces  and  points  con- 
tained in  the  given  evolution,  and  of  their  relative  values 
and  relations  to  each  other,  is  imperative. 

Hence  the  student  of  Major  Tactics  should  be  en- 
tirely familiar  with  these  facts  :  — 

Whatever  the  geometric  plane,  whether  strategic, 
tactical,  or  logistic,  no  evolution  is  valid  unless  there 
exists  in  the  adverse  position  what  is  termed  in  "  The 
Grand  Tactics  of  Chess  "  a  strategetic  weakness. 

Assuming,  however,  that  such  a  defect  exists  in  the 
opposing  force,  and  that  an  evolution  is  valid,  it  is 
then  necessary  to  determine  the  line  of  operations. 
(See  "  Grand  Tactics,"  p.  318.)  If  the  object  of  the 
latter  is  to  checkmate  the  adverse  King,  it  is  a  strategic 
line  of  operations  ;  if  its  object  is  to  queen  a  kindred 
pawn,  it  is  a  logistic  line  of  operations ;  if  its  object  is 
to  capture  a  hostile  piece,  it  is  a  tactical  line  of 
operations. 

The  line  of  operations  being  determined,  it  only  re- 
mains to  indicate  the  initial  evolution  and  the  geometric 
plane  appertaining  thereto. 

Whatever  may  be  the  nature  of  the  geometric  plane 
upon  the  surface  of  which  it  is  required  in  any  given 
situation  to  execute  an  evolution,  the  following  condi- 
tions always  exist :  — 

The  Prime  Tactical  Factor  always  is  that  kindred 
pawn  or  piece  which  captures  the  adverse  Piece  Ex- 
posed ;  or  which  becomes  a  Queen  or  any  other  desired 
kindred  piece  by  occupying  the  Point  of  Junction;  or 
which  checkmates  the  adverse  King.  The  Prime  Tacti- 
cal Factor  always  makes  the  final  move  in  an  evolution; 
it  always  is  posted  either  on  the  central  point  or  on  the 
perimeter  of  its  own  geometric  symbol,  and  its  objective 


LOGISTICS   OF  GEOMETRIC  PLANES.  271 

always  is  the  Point  of  Command,  which  latter  always  is 
the  central  point  of  the  geometric  symbol  appertaining 
to  the  Prime  Tactical  Factor. 

The  Prime  Radii  of  Offence  always  extend  from  the 
Point  of  Command,  as  a  common  centre,  to  the  perimeter 
of  the  geometric  symbol  appertaining  to  the  Prime 
Tactical  Factor,  and  upon  the  vertices  of  this  geometric 
symbol  are  to  be  found  the  Points  Material  in  every 
valid  evolution. 

The  Point  of  Co-operation  always  is  either  coincident 
with  a  Point  Material  or  is  a  point  on  the  perimeter  of 
that  geometric  symbol  appertaining  to  the  Prime  Tacti- 
cal Factor  of  which  the  Point  of  Command  is  the  central 
point ;  it  always  is  an  extremity  of  the  Supporting 
Front,  and  it  always  is  united,  either  by  a  vertical,  a 
horizontal,  a  diagonal,  or  an  oblique,  with  the  Support- 
ing Origin. 

The  nature  of  a  Geometric  Plane  always  is  determined 
by  the  nature  of  the  existing  tactical  defect ;  the  nature 
of  the  Geometric  Plane  determines  the  selection  of  the 
Prime  Tactical  Factor,  and  the  character  of  the  geo- 
metric symbol  of  the  Prime  Tactical  Factor  determines 
the  nature  of  the  evolution. 

The  student,  therefore,  has  only  to  locate  a  tactical 
defect  in  the  adverse  position  and  to  proceed  as  follows  • 


RULES  OF  MAJOR  TACTICS. 

Whenever  a  tactical    defect  exists   in  the    adverse 
position :  — 

I.  Locate  the  Piece  Exposed  and  the  Prime  Tactical 
Factor. 

II.  Indicate  the  Primary  Origin  and  the  Points  Mate- 
rial and  describe  that  geometric  symbol  which  apper- 


272  MAJOR  TACTICS. 

tains  to    the    Prime    Tactical    Factor    and    upon    the 
perimeter  of  which  the  Points  Material  are  situated. 

III.  Taking  the  Primary  Origin,  then  indicate  the 
Point  of  Command  and  describe  the  Front  Offensive. 

IV.  Taking  the  Point  of  Command  as  the  centre  and 
the  Points  Material  as  the  vertices  of  that  logistic  sym- 
bol which  appertains  to  the   Prime    Tactical  Factor, 
describe  the  Front  Defensive  and  the  Prime  Radii  of 
Offence. 

V.  Locate  the  Supporting  Factor,  then  indicate  the 
Point  of  Co-operation  and  the  Supporting  Origin,  and 
describe  the  Supporting  Front. 

VI.  Locate  the    Disturbing  Factors,  then    indicate 
the  Points  of  Interference  and  describe  the  Front  of 
Interference. 

VII.  Taking  the  Fronts  of  Interference,  locate  the 
Auxiliary  Factors  ;  then  indicate  the  Auxiliary  Origins 
and  describe  the  Auxiliary  Fronts. 

VIII.  Taking  the  Front  Offensive,  the  Front  Defen- 
sive, the  Supporting  Front,  the  Fronts  Auxiliary,  and 
the  Fronts  of  Interference,  describe  the  Tactical  Front. 

Then,  if  the  number  of  kindred  radii  of  offence  which 
are  directly  or  indirectly  attacking  the  Point  of  Com- 
mand, exceed  the  number  of  adverse  radii  of  defence 
which  directly  or  indirectly  are  defending  the  Point  of 
Command,  the  Prime  Tactical  Factor  may  occupy  the 
Point  of  Command  without  capture,  which  latter  is  the 
end  and  aim  of  every  evolution  of  Major  Tactics. 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

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